Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
28101	Evaluate the Integral	integral of (9x^4)/( square root of x^5-1) with respect to x	$\int \frac{9 x^{4}}{\sqrt{x^{5} - 1}} d x$
28102	Evaluate the Integral	integral of (8x+3)/((20x^2+15x)^7) with respect to x	$\int \frac{8 x + 3}{{(20 x^{2} + 15 x)}^{7}} d x$
28103	Evaluate the Integral	integral of (cos( square root of 5t))/( square root of 5t) with respect to t	$\int \frac{\cos (\sqrt{5 t})}{\sqrt{5 t}} d t$
28104	Evaluate the Integral	integral of (cos( square root of 6t))/( square root of 6t) with respect to t	$\int \frac{\cos (\sqrt{6 t})}{\sqrt{6 t}} d t$
28105	Evaluate the Integral	integral of ax^4+bx^3+3c with respect to x	$\int a x^{4} + b x^{3} + 3 c d x$
28106	Evaluate the Integral	integral of ce^(-x) with respect to x	$\int c e^{- x} d x$
28107	Evaluate the Integral	integral of (arctan(y))/(1+y^2) with respect to y	$\int \frac{\arctan (y)}{1 + y^{2}} d y$
28108	Evaluate the Integral	integral of (arctan(7x))/(1+49x^2) with respect to x	$\int \frac{\arctan (7 x)}{1 + 49 x^{2}} d x$
28109	Evaluate the Integral	integral of (arcsin(2x))/( square root of 1-4x^2) with respect to x	$\int \frac{\arcsin (2 x)}{\sqrt{1 - 4 x^{2}}} d x$
28110	Evaluate the Integral	integral of (9x+5)/((9x^2+10x)^5) with respect to x	$\int \frac{9 x + 5}{{(9 x^{2} + 10 x)}^{5}} d x$
28111	Evaluate the Integral	integral of (cos(x))/(8sin(x)^2+9sin(x)) with respect to x	$\int \frac{\cos (x)}{8 \sin^{2} (x) + 9 \sin (x)} d x$
28112	Evaluate the Integral	integral of cos(x)^2sin(x)^4 with respect to x	$\int \cos^{2} (x) \sin^{4} (x) d x$
28113	Evaluate the Integral	integral of (cos(x))/(4-sin(x)^2) with respect to xdx	$\int \frac{\cos (x)}{4 - \sin^{2} (x)} d x d x$
28114	Evaluate the Integral	integral of cos(4x)^2 with respect to x	$\int \cos^{2} (4 x) d x$
28115	Evaluate the Integral	integral of cos(x)^2+sin(x)^2 with respect to x	$\int \cos^{2} (x) + \sin^{2} (x) d x$
28116	Evaluate the Integral	integral of cos(x)^17sin(x) with respect to x	$\int \cos^{17} (x) \sin (x) d x$
28117	Evaluate the Integral	integral of cos(2x)^2sin(2x) with respect to x	$\int \cos^{2} (2 x) \sin (2 x) d x$
28118	Evaluate the Integral	integral of cos(x)^14sin(x) with respect to x	$\int \cos^{14} (x) \sin (x) d x$
28119	Evaluate the Integral	integral of cos(6x)^2 with respect to x	$\int \cos^{2} (6 x) d x$
28120	Evaluate the Integral	integral of (cos(2x))/(sin(2x)) with respect to x	$\int \frac{\cos (2 x)}{\sin (2 x)} d x$
28121	Evaluate the Integral	integral of (cos(5x))/(sin(5x)) with respect to x	$\int \frac{\cos (5 x)}{\sin (5 x)} d x$
28122	Evaluate the Integral	integral of (cos(5x))/(sin(5x))*cos(5x) with respect to x	$\int \frac{\cos (5 x)}{\sin (5 x)} \cdot \cos (5 x) d x$
28123	Evaluate the Integral	integral of (cos(4x))/2 with respect to x	$\int \frac{\cos (4 x)}{2} d x$
28124	Evaluate the Integral	integral of (cos(x))/((2sin(x)-1)^3) with respect to x	$\int \frac{\cos (x)}{{(2 \sin (x) - 1)}^{3}} d x$
28125	Evaluate the Integral	integral of (-cos(x))/(sin(x)^6) with respect to x	$\int \frac{- \cos (x)}{\sin^{6} (x)} d x$
28126	Evaluate the Integral	integral of (cos(x))/(sin(x)^10) with respect to x	$\int \frac{\cos (x)}{\sin^{10} (x)} d x$
28127	Evaluate the Integral	integral of (8z^3-8)/( square root of z^4-4z) with respect to z	$\int \frac{8 z^{3} - 8}{\sqrt{z^{4} - 4 z}} d z$
28128	Evaluate the Integral	integral of (8y^3)/((2y^4-3)^6) with respect to y	$\int \frac{8 y^{3}}{{(2 y^{4} - 3)}^{6}} d y$
28129	Evaluate the Integral	integral of 7/x-9e^(5x)+ square root of x^5 with respect to x	$\int \frac{7}{x} - 9 e^{5 x} + \sqrt{x^{5}} d x$
28130	Evaluate the Integral	integral of (9r^2)/( square root of 1-r^3) with respect to r	$\int \frac{9 r^{2}}{\sqrt{1 - r^{3}}} d r$
28131	Evaluate the Integral	integral of 8/(x^5) with respect to x	$\int \frac{8}{x^{5}} d x$
28132	Evaluate the Integral	integral of (6x)/((x^2+1)^2) with respect to x	$\int \frac{6 x}{{(x^{2} + 1)}^{2}} d x$
28133	Evaluate the Integral	integral of (6x)/((3x^2-5)^4) with respect to x	$\int \frac{6 x}{{(3 x^{2} - 5)}^{4}} d x$
28134	Evaluate the Integral	integral of (6x)/(3x^2+1) with respect to x	$\int \frac{6 x}{3 x^{2} + 1} d x$
28135	Evaluate the Integral	integral of (6x)/(3x^2+5) with respect to x	$\int \frac{6 x}{3 x^{2} + 5} d x$
28136	Evaluate the Integral	integral of (6x+12)/( square root of x^2+4x-1) with respect to x	$\int \frac{6 x + 12}{\sqrt{x^{2} + 4 x - 1}} d x$
28137	Evaluate the Integral	integral of (7e^(7y))/(2+e^(7y)) with respect to y	$\int \frac{7 e^{7 y}}{2 + e^{7 y}} d y$
28138	Evaluate the Integral	integral of (7x^6)/((3+x^7)^3) with respect to x	$\int \frac{7 x^{6}}{{(3 + x^{7})}^{3}} d x$
28139	Evaluate the Integral	integral of (7x^6)/(x^7 square root of 16x^14-17) with respect to x	$\int \frac{7 x^{6}}{x^{7} \sqrt{16 x^{14} - 17}} d x$
28140	Evaluate the Integral	integral of 7/((z-10)^7) with respect to z	$\int \frac{7}{{(z - 10)}^{7}} d z$
28141	Evaluate the Integral	integral of 7/(9+7x) with respect to x	$\int \frac{7}{9 + 7 x} d x$
28142	Evaluate the Integral	integral of 7^(3x) with respect to x	$\int 7^{3 x} d x$
28143	Evaluate the Integral	integral from (7pi)/6 to (11pi)/6 of 5csc(x)cot(x) with respect to x	$\int_{\frac{7 π}{6}}^{\frac{11 π}{6}} 5 \csc (x) \cot (x) d x$
28144	Evaluate the Integral	integral of 7/(x^2+3x-10) with respect to x	$\int \frac{7}{x^{2} + 3 x - 10} d x$
28145	Evaluate the Integral	integral of 6/x+3/(x^2)+ square root of x-6e^(-2x)+9 with respect to x	$\int \frac{6}{x} + \frac{3}{x^{2}} + \sqrt{x} - 6 e^{- 2 x} + 9 d x$
28146	Evaluate the Integral	integral of -6000/(x^2) with respect to x	$\int - \frac{6000}{x^{2}} d x$
28147	Evaluate the Integral	integral of (6cos(t))/((2+sin(t))^2) with respect to t	$\int \frac{6 \cos (t)}{{(2 + \sin (t))}^{2}} d t$
28148	Evaluate the Integral	integral of (6x^2-16x+2)/(x^3-4x^2+x+6) with respect to x	$\int \frac{6 x^{2} - 16 x + 2}{x^{3} - 4 x^{2} + x + 6} d x$
28149	Evaluate the Integral	integral of 6/( square root of 5^2-36x^2) with respect to x	$\int \frac{6}{\sqrt{5^{2} - 36 x^{2}}} d x$
28150	Evaluate the Integral	integral of 6/(x^2+1) with respect to x	$\int \frac{6}{x^{2} + 1} d x$
28151	Evaluate the Integral	integral of 6/((9t^2+1)^2) with respect to t	$\int \frac{6}{{(9 t^{2} + 1)}^{2}} d t$
28152	Evaluate the Integral	integral of (6e^(-1/x))/(x^2) with respect to x	$\int \frac{6 e^{- \frac{1}{x}}}{x^{2}} d x$
28153	Evaluate the Integral	integral of (6x^2-2x-1)/(4x^3-x) with respect to x	$\int \frac{6 x^{2} - 2 x - 1}{4 x^{3} - x} d x$
28154	Evaluate the Integral	integral of (6x^3-5)/(x^2) with respect to x	$\int \frac{6 x^{3} - 5}{x^{2}} d x$
28155	Evaluate the Integral	integral of (6x^3-6x^2+x)/x with respect to x	$\int \frac{6 x^{3} - 6 x^{2} + x}{x} d x$
28156	Evaluate the Integral	integral of (5x-12)/(x(x-4)) with respect to x	$\int \frac{5 x - 12}{x (x - 4)} d x$
28157	Evaluate the Integral	integral of (5x-2)/(x^2-4) with respect to x	$\int \frac{5 x - 2}{x^{2} - 4} d x$
28158	Evaluate the Integral	integral of 5e^(3x) with respect to x	$\int 5 e^{3 x} d x$
28159	Evaluate the Integral	integral of 5^3 square root of x^2 with respect to x	$\int 5^{3} \sqrt{x^{2}} d x$
28160	Evaluate the Integral	integral of 5/(x^6) with respect to x	$\int \frac{5}{x^{6}} d x$
28161	Evaluate the Integral	integral of 5/(4x-1) with respect to x	$\int \frac{5}{4 x - 1} d x$
28162	Evaluate the Integral	integral of 5/( fifth root of x^4) with respect to x	$\int \frac{5}{\sqrt[5]{x^{4}}} d x$
28163	Evaluate the Integral	integral of 5/( square root of 9-x^2) with respect to x	$\int \frac{5}{\sqrt{9 - x^{2}}} d x$
28164	Evaluate the Integral	integral of (5x^2)/(3x^3-8) with respect to x	$\int \frac{5 x^{2}}{3 x^{3} - 8} d x$
28165	Evaluate the Integral	integral of 5/( square root of 36-x^2) with respect to x	$\int \frac{5}{\sqrt{36 - x^{2}}} d x$
28166	Evaluate the Integral	integral of (4x^2-2x+1)/(4x^3-x) with respect to x	$\int \frac{4 x^{2} - 2 x + 1}{4 x^{3} - x} d x$
28167	Evaluate the Integral	integral of (4x^2-4x+6)/(x^3-x^2-6x) with respect to x	$\int \frac{4 x^{2} - 4 x + 6}{x^{3} - x^{2} - 6 x} d x$
28168	Evaluate the Integral	integral of 4^(-4x) with respect to x	$\int 4^{- 4 x} d x$
28169	Evaluate the Integral	integral of (4x)/((x-1)^2(x+1)) with respect to x	$\int \frac{4 x}{{(x - 1)}^{2} (x + 1)} d x$
28170	Evaluate the Integral	integral of 4e^(9x) with respect to x	$\int 4 e^{9 x} d x$
28171	Evaluate the Integral	integral of (4x+6)/((x^2+3x+7)^3) with respect to x	$\int \frac{4 x + 6}{{(x^{2} + 3 x + 7)}^{3}} d x$
28172	Evaluate the Integral	integral of (4x+7)/((4x^2+14x)^4) with respect to x	$\int \frac{4 x + 7}{{(4 x^{2} + 14 x)}^{4}} d x$
28173	Evaluate the Integral	integral of (4x-1)/(x^2+x-2) with respect to x	$\int \frac{4 x - 1}{x^{2} + x - 2} d x$
28174	Evaluate the Integral	integral of (4x)/(5+2x+x^2) with respect to x	$\int \frac{4 x}{5 + 2 x + x^{2}} d x$
28175	Evaluate the Integral	integral of (5x^2+20x+6)/(x^3+2x^2+x) with respect to x	$\int \frac{5 x^{2} + 20 x + 6}{x^{3} + 2 x^{2} + x} d x$
28176	Evaluate the Integral	integral of (5x^4-7x^2+9)/(x^2) with respect to x	$\int \frac{5 x^{4} - 7 x^{2} + 9}{x^{2}} d x$
28177	Evaluate the Integral	integral of (5y^4)/(y^5-15) with respect to ydx	$\int \frac{5 y^{4}}{y^{5} - 15} d y d x$
28178	Evaluate the Integral	integral of (x^3+ square root of x)/( cube root of x^2) with respect to x	$\int \frac{x^{3} + \sqrt{x}}{\sqrt[3]{x^{2}}} d x$
28179	Evaluate the Integral	integral of (x^3+27)/(x+3) with respect to x	$\int \frac{x^{3} + 27}{x + 3} d x$
28180	Evaluate the Integral	integral of (x^3+1)/(x^2-1) with respect to x	$\int \frac{x^{3} + 1}{x^{2} - 1} d x$
28181	Evaluate the Integral	integral of (x^3)/3*(1/x) with respect to x	$\int \frac{x^{3}}{3} \cdot (\frac{1}{x}) d x$
28182	Evaluate the Integral	integral of (x^3-125)/(x-5) with respect to x	$\int \frac{x^{3} - 125}{x - 5} d x$
28183	Evaluate the Integral	integral of (x^3-2 square root of x)/x with respect to x	$\int \frac{x^{3} - 2 \sqrt{x}}{x} d x$
28184	Evaluate the Integral	integral of (x^3-2x^2+3)/(x-2) with respect to x	$\int \frac{x^{3} - 2 x^{2} + 3}{x - 2} d x$
28185	Find Where Increasing/Decreasing Using Derivatives	f(x)=3x^4+8x^3	$f (x) = 3 x^{4} + 8 x^{3}$
28186	Evaluate the Integral	integral of (x^3+2x)/(x^4+4x^2+7) with respect to x	$\int \frac{x^{3} + 2 x}{x^{4} + 4 x^{2} + 7} d x$
28187	Evaluate the Integral	integral of (x^3)/(x^2+10) with respect to x	$\int \frac{x^{3}}{x^{2} + 10} d x$
28188	Evaluate the Integral	integral of (x^3)/( cube root of (x^2+1)^2) with respect to x	$\int \frac{x^{3}}{\sqrt[3]{{(x^{2} + 1)}^{2}}} d x$
28189	Evaluate the Integral	integral of (x^3)/( square root of 9-x^2) with respect to x	$\int \frac{x^{3}}{\sqrt{9 - x^{2}}} d x$
28190	Evaluate the Integral	integral of (x^3)/(100+x^2) with respect to x	$\int \frac{x^{3}}{100 + x^{2}} d x$
28191	Evaluate the Integral	integral of (x^3)/( square root of x^2+121) with respect to x	$\int \frac{x^{3}}{\sqrt{x^{2} + 121}} d x$
28192	Evaluate the Integral	integral of (x^3)/( square root of x^2+16) with respect to x	$\int \frac{x^{3}}{\sqrt{x^{2} + 16}} d x$
28193	Evaluate the Integral	integral of (x^3)/( square root of x^2-4) with respect to x	$\int \frac{x^{3}}{\sqrt{x^{2} - 4}} d x$
28194	Evaluate the Integral	integral of (x^4+3x^3-5x^2-4x+5)/(x^3-5) with respect to x	$\int \frac{x^{4} + 3 x^{3} - 5 x^{2} - 4 x + 5}{x^{3} - 5} d x$
28195	Evaluate the Integral	integral of (x^4)/(x^2+4) with respect to x	$\int \frac{x^{4}}{x^{2} + 4} d x$
28196	Evaluate the Integral	integral of (x^4)/(x^2+64) with respect to x	$\int \frac{x^{4}}{x^{2} + 64} d x$
28197	Evaluate the Integral	integral of (x^3-8)/(x-2) with respect to x	$\int \frac{x^{3} - 8}{x - 2} d x$
28198	Evaluate the Integral	integral of (x^3-8x)/(2x^2) with respect to x	$\int \frac{x^{3} - 8 x}{2 x^{2}} d x$
28199	Evaluate the Integral	integral of (x^3-x+3)/(x^2+x-2) with respect to x	$\int \frac{x^{3} - x + 3}{x^{2} + x - 2} d x$
28200	Evaluate the Integral	integral of (x^3-4x^2-4x+20)/(x^2-5) with respect to x	$\int \frac{x^{3} - 4 x^{2} - 4 x + 20}{x^{2} - 5} d x$