Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
26001	Evaluate the Integral	integral of e^(2x)sin(e^x) with respect to x	$\int e^{2 x} \sin (e^{x}) d x$
26002	Evaluate the Limit	limit as x approaches 0 of (cot(3x))/(cot(x))	$lim_{x \to 0} \frac{\cot (3 x)}{\cot (x)}$
26003	Evaluate the Integral	integral of (sin(5/x))/(x^2) with respect to x	$\int \frac{\sin (\frac{5}{x})}{x^{2}} d x$
26004	Evaluate the Limit	limit as x approaches 1 of (x^2+2x-3)/(x-1)	$lim_{x \to 1} \frac{x^{2} + 2 x - 3}{x - 1}$
26005	Evaluate the Limit	limit as x approaches infinity of arctan(x^5-x^9)	$lim_{x \to \infty} \arctan (x^{5} - x^{9})$
26006	Evaluate the Integral	integral of ( natural log of 1+ square root of x)/( square root of x) with respect to x	$\int \frac{\ln (1 + \sqrt{x})}{\sqrt{x}} d x$
26007	Evaluate the Integral	integral of ( natural log of 3t-5)/(3t-5) with respect to t	$\int \frac{\ln (3 t - 5)}{3 t - 5} d t$
26008	Evaluate the Integral	integral of ( natural log of 3x)/(x^2) with respect to x	$\int \frac{\ln (3 x)}{x^{2}} d x$
26009	Evaluate the Limit	limit as h approaches 0 of (1/(2+h)-1/2)/h	$lim_{h \to 0} \frac{\frac{1}{2 + h} - \frac{1}{2}}{h}$
26010	Evaluate the Integral	integral of ( natural log of x^3)/(8x) with respect to x	$\int \frac{\ln (x^{3})}{8 x} d x$
26011	Evaluate the Integral	integral of e^z with respect to z	$\int e^{z} d z$
26012	Evaluate the Integral	integral of ( natural log of 9x)/x with respect to x	$\int \frac{\ln (9 x)}{x} d x$
26013	Evaluate the Limit	limit as x approaches infinity of ( square root of 9x^6-x)/(x^3+3)	$lim_{x \to \infty} \frac{\sqrt{9 x^{6} - x}}{x^{3} + 3}$
26014	Evaluate the Integral	integral of e^(3x)cos(h(2x)) with respect to x	$\int e^{3 x} \cosh (2 x) d x$
26015	Evaluate the Integral	integral of e^(-3x)sin(x) with respect to x	$\int e^{- 3 x} \sin (x) d x$
26016	Find the Local Maxima and Minima	f(x)=2x^4-20x^2+18	$f (x) = 2 x^{4} - 20 x^{2} + 18$
26017	Find the Local Maxima and Minima	f(x)=x^(4/3)-x^(2/3)	$f (x) = x^{\frac{4}{3}} - x^{\frac{2}{3}}$
26018	Evaluate the Integral	integral of e^tcot(e^t-4) with respect to t	$\int e^{t} \cot (e^{t} - 4) d t$
26019	Evaluate the Integral	integral of e^(kx) with respect to x	$\int e^{k x} d x$
26020	Evaluate the Integral	integral of 1/(7x^4) with respect to x	$\int \frac{1}{7 x^{4}} d x$
26021	Find the Derivative - d/dx	y=x(x^4+4)^3	$y = x {(x^{4} + 4)}^{3}$
26022	Evaluate the Integral	integral of 1/(9-x^2) with respect to x	$\int \frac{1}{9 - x^{2}} d x$
26023	Evaluate the Integral	integral of 1/(5-2x) with respect to x	$\int \frac{1}{5 - 2 x} d x$
26024	Find the Derivative - d/dx	y=10	$y = 10$
26025	Evaluate the Integral	integral of 1/(x square root of 9-4x^2) with respect to x	$\int \frac{1}{x \sqrt{9 - 4 x^{2}}} d x$
26026	Evaluate the Integral	integral of 1/x with respect to y	$\int \frac{1}{x} d y$
26027	Evaluate the Integral	integral of 1/(x natural log of 4x) with respect to x	$\int \frac{1}{x \ln (4 x)} d x$
26028	Evaluate the Integral	integral of 1/Z with respect to x	$\int \frac{1}{Z} d x$
26029	Find the Derivative - d/dx	tan(x)cot(x)	$\tan (x) \cot (x)$
26030	Evaluate the Integral	integral of 1/(x( natural log of (x)^2)) with respect to x	$\int \frac{1}{x (\ln ({(x)}^{2}))} d x$
26031	Evaluate the Integral	integral of 1/(x(1+x^2)) with respect to x	$\int \frac{1}{x (1 + x^{2})} d x$
26032	Evaluate the Integral	integral of 23/(x^2) with respect to x	$\int \frac{23}{x^{2}} d x$
26033	Evaluate the Integral	integral of (24x^3+20x)/(3x^4+5x^2) with respect to x	$\int \frac{24 x^{3} + 20 x}{3 x^{4} + 5 x^{2}} d x$
26034	Find the x and y Intercepts	3x(x-3)^3	$3 x {(x - 3)}^{3}$
26035	Evaluate the Integral	integral of 2/5*(sec(x)tan(x)) with respect to x	$\int \frac{2}{5} \cdot (\sec (x) \tan (x)) d x$
26036	Find dp/dq	p=((q^7+4)/(2q))((q^6+6)/q)	$p = (\frac{q^{7} + 4}{2 q}) (\frac{q^{6} + 6}{q})$
26037	Evaluate the Integral	integral of (11x)/(x-10) with respect to x	$\int \frac{11 x}{x - 10} d x$
26038	Find dy/dx	y = square root of natural log of 3x	$y = \sqrt{\ln (3 x)}$
26039	Find dy/dx	y=x^0.35	$y = x^{0.35}$
26040	Evaluate the Integral	integral of (1+x)/(1-x) with respect to x	$\int \frac{1 + x}{1 - x} d x$
26041	Evaluate the Integral	integral of (1+10t^7)/(9t) with respect to t	$\int \frac{1 + 10 t^{7}}{9 t} d t$
26042	Find the Tangent Line at (2,0)	y=x^3-4x at the point (2,0)	$\int \frac{12 x}{\sqrt{1 - 36 x^{4}}} d x$
26043	Evaluate the Integral	integral of (2x^2-9x-35)/((x+1)(x+2)(x+3)) with respect to x	$\int \frac{2 x^{2} - 9 x - 35}{(x + 1) (x + 2) (x + 3)} d x$
26044	Evaluate the Limit	limit as x approaches 3 of (2x^2-18)/(x^2-4x+3)	$lim_{x \to 3} \frac{2 x^{2} - 18}{x^{2} - 4 x + 3}$
26045	Evaluate the Integral	integral of (2x)/( square root of 16-9x^2) with respect to x	$\int \frac{2 x}{\sqrt{16 - 9 x^{2}}} d x$
26046	Evaluate the Integral	integral of (3x^4+2x^3+6)/(x^5+5x^4+10x+12) with respect to x	$\int \frac{3 x^{4} + 2 x^{3} + 6}{x^{5} + 5 x^{4} + 10 x + 12} d x$
26047	Evaluate the Integral	integral of (-27x^2)/((9-9x^3)^2) with respect to x	$\int \frac{- 27 x^{2}}{{(9 - 9 x^{3})}^{2}} d x$
26048	Evaluate the Integral	integral of 3/(x^2+9) with respect to x	$\int \frac{3}{x^{2} + 9} d x$
26049	Evaluate the Integral	integral of 3/(16+x^2) with respect to x	$\int \frac{3}{16 + x^{2}} d x$
26050	Evaluate the Integral	integral of 300/((3x+25)^2) with respect to x	$\int \frac{300}{{(3 x + 25)}^{2}} d x$
26051	Evaluate the Integral	integral of 36/((2x-3)^2) with respect to x	$\int \frac{36}{{(2 x - 3)}^{2}} d x$
26052	Evaluate the Integral	integral of (3t-2)/(t+1) with respect to t	$\int \frac{3 t - 2}{t + 1} d t$
26053	Evaluate the Integral	integral of (3x+4)/(x^3-2x-4) with respect to x	$\int \frac{3 x + 4}{x^{3} - 2 x - 4} d x$
26054	Evaluate the Integral	integral of (3x-3)/((x-2x+1)^2) with respect to x	$\int \frac{3 x - 3}{{(x - 2 x + 1)}^{2}} d x$
26055	Evaluate the Integral	integral of (4x^2-3x-4)/(x^3+x^2-2x) with respect to x	$\int \frac{4 x^{2} - 3 x - 4}{x^{3} + x^{2} - 2 x} d x$
26056	Evaluate the Integral	integral of 4/(5x-3) with respect to x	$\int \frac{4}{5 x - 3} d x$
26057	Evaluate the Integral	integral of 5/(2x-1) with respect to x	$\int \frac{5}{2 x - 1} d x$
26058	Evaluate the Integral	integral of (5x+3)/(x^2+2x-3) with respect to x	$\int \frac{5 x + 3}{x^{2} + 2 x - 3} d x$
26059	Evaluate the Integral	integral of 7/(2+7x) with respect to x	$\int \frac{7}{2 + 7 x} d x$
26060	Evaluate the Integral	integral of (7x^2-9x+54)/((x-3)*(x^2+9)) with respect to x	$\int \frac{7 x^{2} - 9 x + 54}{(x - 3) \cdot (x^{2} + 9)} d x$
26061	Evaluate the Integral	integral of 4/(x^2-4) with respect to x	$\int \frac{4}{x^{2} - 4} d x$
26062	Find the Derivative of the Integral	integral from 0 to 7 of square root of 49-x^2 with respect to x	$\int_{0}^{7} \sqrt{49 - x^{2}} d x$
26063	Find the Derivative of the Integral	integral from 0 to R of (r^3)/(R-r) with respect to r	$\int_{0}^{R} \frac{r^{3}}{R - r} d r$
26064	Find the Derivative of the Integral	integral from 1 to x^2 of square root of 3+r^3 with respect to r	$\int_{1}^{x^{2}} \sqrt{3 + r^{3}} d r$
26065	Find the Derivative of the Integral	integral from 0 to 4 of square root of 16-x^2 with respect to x	$\int_{0}^{4} \sqrt{16 - x^{2}} d x$
26066	Find the Derivative of the Integral	integral from 0 to 3 of 12x^2e^(x^3) with respect to x	$\int_{0}^{3} 12 x^{2} e^{x^{3}} d x$
26067	Find the Derivative of the Integral	integral from 0 to 2pi of \|cos(x)\| with respect to x	$\int_{0}^{2 π} \| \cos (x) \| d x$
26068	Find the Derivative of the Integral	integral from 0 to 3x of square root of 1+t^2 with respect to t	$\int_{0}^{3 x} \sqrt{1 + t^{2}} d t$
26069	Find the Derivative of the Integral	integral from 0 to 1 of 1/( square root of x) with respect to x	$\int_{0}^{1} \frac{1}{\sqrt{x}} d x$
26070	Find the Derivative of the Integral	integral from 0 to x^2 of cos(t^2+1) with respect to t	$\int_{0}^{x^{2}} \cos (t^{2} + 1) d t$
26071	Find the Derivative of the Integral	integral from 0 to 1 of 4x^5-5x^4 with respect to x	$\int_{0}^{1} 4 x^{5} - 5 x^{4} d x$
26072	Find the Derivative of the Integral	integral from 0 to 1 of (e^x)/(1+e^(2x)) with respect to x	$\int_{0}^{1} \frac{e^{x}}{1 + e^{2 x}} d x$
26073	Find the Derivative of the Integral	integral from 0 to 1 of 6x-2x^3-x square root of x+3e^x with respect to x	$\int_{0}^{1} 6 x - 2 x^{3} - x \sqrt{x} + 3 e^{x} d x$
26074	Find the Derivative of the Integral	integral from 0 to 1 of e^x with respect to x	$\int_{0}^{1} e^{x} d x$
26075	Find the Derivative of the Integral	integral from 0 to 1 of y/(e^(2y)) with respect to y	$\int_{0}^{1} \frac{y}{e^{2 y}} d y$
26076	Find the Derivative of the Integral	integral from 0 to 1 of 2xe^(x^2) with respect to x	$\int_{0}^{1} 2 x e^{x^{2}} d x$
26077	Find the Derivative of the Integral	integral from 0 to 1 of f(t) with respect to t	$\int_{0}^{1} f (t) d t$
26078	Find the Derivative of the Integral	integral from 0 to 20 of square root of 5x with respect to x	$\int_{0}^{20} \sqrt{5 x} d x$
26079	Find the Derivative of the Integral	integral from 0 to 2pi of 8cos(2t) with respect to t	$\int_{0}^{2 π} 8 \cos (2 t) d t$
26080	Find the Derivative of the Integral	integral from 0 to 2pi of sin(x) with respect to x	$\int_{0}^{2 π} \sin (x) d x$
26081	Find the Derivative of the Integral	integral from 0 to 2 of 6x^2 with respect to x	$\int_{0}^{2} 6 x^{2} d x$
26082	Find the Derivative of the Integral	integral from 0 to 10 of \|x-5\| with respect to x	$\int_{0}^{10} \| x - 5 \| d x$
26083	Find the Derivative of the Integral	integral from 0 to 10 of e^(-x^2) with respect to x	$\int_{0}^{10} e^{- x^{2}} d x$
26084	Find the Derivative of the Integral	integral of 1/(x natural log of x^2) with respect to x	$\int \frac{1}{x \ln (x^{2})} d x$
26085	Find the Derivative of the Integral	integral of e^(2x)cos(3x) with respect to x	$\int e^{2 x} \cos (3 x) d x$
26086	Find the Derivative of the Integral	integral of e^(3x)cos(2x) with respect to x	$\int e^{3 x} \cos (2 x) d x$
26087	Find the Derivative of the Integral	integral of 1/(t square root of 2t) with respect to tdt	$\int \frac{1}{t \sqrt{2 t}} d t d t$
26088	Find the Derivative of the Integral	integral of cos(4x)^3 with respect to x	$\int \cos^{3} (4 x) d x$
26089	Find the Derivative of the Integral	integral of (cos(8x))/( square root of 1+sin(8x)) with respect to x	$\int \frac{\cos (8 x)}{\sqrt{1 + \sin (8 x)}} d x$
26090	Find the Derivative of the Integral	integral of (cos(h( natural log of x)))/x with respect to x	$\int \frac{\cosh (\ln (x))}{x} d x$
26091	Find the Derivative of the Integral	integral of 1/(cos(3x+1)^2) with respect to xdx	$\int \frac{1}{\cos^{2} (3 x + 1)} d x d x$
26092	Find the Derivative of the Integral	integral of (6+x^2)/x with respect to x	$\int \frac{6 + x^{2}}{x} d x$
26093	Find the Derivative of the Integral	integral of 8/( seventh root of x^6) with respect to x	$\int \frac{8}{\sqrt[7]{x^{6}}} d x$
26094	Find the Derivative of the Integral	integral from pi/3 to 2/pi of 3cos(x)^2sin(x) with respect to x	$\int_{\frac{π}{3}}^{\frac{2}{π}} 3 \cos^{2} (x) \sin (x) d x$
26095	Find the Derivative of the Integral	integral of e^x square root of 1+e^x with respect to x	$\int e^{x} \sqrt{1 + e^{x}} d x$
26096	Find the Derivative of the Integral	integral of e^(4x^2) with respect to x	$\int e^{4 x^{2}} d x$
26097	Find the Derivative of the Integral	integral of sec(x)^3 with respect to x	$\int \sec^{3} (x) d x$
26098	Find the Derivative of the Integral	integral of (sin(20t))/(sin(10t)) with respect to t	$\int \frac{\sin (20 t)}{\sin (10 t)} d t$
26099	Find the Derivative of the Integral	integral of (sec(x))/(sec(x)-cos(x)) with respect to x	$\int \frac{\sec (x)}{\sec (x) - \cos (x)} d x$
26100	Find the Derivative of the Integral	integral of t^3tan(t) with respect to t	$\int t^{3} \tan (t) d t$