Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
28001	Evaluate the Integral	integral of sec(2x)^2e^(tan(2x)) with respect to x	$\int \sec^{2} (2 x) e^{\tan (2 x)} d x$
28002	Evaluate the Integral	integral from 1 to 2 of x^3 natural log of x with respect to x	$\int_{1}^{2} x^{3} \ln (x) d x$
28003	Evaluate the Integral	integral of pi^x-cos(x) with respect to x	$\int π^{x} - \cos (x) d x$
28004	Evaluate the Integral	integral of s/( cube root of 1-2s^2) with respect to s	$\int \frac{s}{\sqrt[3]{1 - 2 s^{2}}} d s$
28005	Evaluate the Integral	integral of p^8 natural log of p with respect to p	$\int p^{8} \ln (p) d p$
28006	Evaluate the Integral	integral from -pi/6 to pi/6 of sec(y)^2 with respect to y	$\int_{- \frac{π}{6}}^{\frac{π}{6}} \sec^{2} (y) d y$
28007	Evaluate the Integral	integral of pe^x with respect to x	$\int p e^{x} d x$
28008	Evaluate the Integral	integral of r^2((r^3)/18-1)^5 with respect to r	$\int r^{2} {(\frac{r^{3}}{18} - 1)}^{5} d r$
28009	Evaluate the Integral	integral of r^2(r^3-2)^2 with respect to r	$\int r^{2} {(r^{3} - 2)}^{2} d r$
28010	Evaluate the Integral	integral of (3x^2-11)/(x^4-1) with respect to x	$\int \frac{3 x^{2} - 11}{x^{4} - 1} d x$
28011	Evaluate the Integral	integral of (3x^3+1)/x with respect to x	$\int \frac{3 x^{3} + 1}{x} d x$
28012	Evaluate the Integral	integral of 3/(t^5) with respect to t	$\int \frac{3}{t^{5}} d t$
28013	Evaluate the Integral	integral of 3/( square root of 1-9x^2) with respect to x	$\int \frac{3}{\sqrt{1 - 9 x^{2}}} d x$
28014	Evaluate the Integral	integral of (3x^3)/( square root of x^2-25) with respect to x	$\int \frac{3 x^{3}}{\sqrt{x^{2} - 25}} d x$
28015	Evaluate the Integral	integral of 3/(116-40x+4x^2) with respect to x	$\int \frac{3}{116 - 40 x + 4 x^{2}} d x$
28016	Evaluate the Integral	integral of 3/((3x-1) natural log of 3x-1) with respect to x	$\int \frac{3}{(3 x - 1) \ln (3 x - 1)} d x$
28017	Evaluate the Integral	integral of (2x-3)/((x-1)^2) with respect to x	$\int \frac{2 x - 3}{{(x - 1)}^{2}} d x$
28018	Evaluate the Integral	integral of (3(x-4))/(x^2-2x-3) with respect to x	$\int \frac{3 (x - 4)}{x^{2} - 2 x - 3} d x$
28019	Evaluate the Integral	integral of (3x^2)/y with respect to y	$\int \frac{3 x^{2}}{y} d y$
28020	Evaluate the Integral	integral of (3x^2)/(x^3-7) with respect to x	$\int \frac{3 x^{2}}{x^{3} - 7} d x$
28021	Evaluate the Integral	integral of (2x-3)/(x^2-5x-6) with respect to x	$\int \frac{2 x - 3}{x^{2} - 5 x - 6} d x$
28022	Evaluate the Integral	integral of (2y)/x with respect to y	$\int \frac{2 y}{x} d y$
28023	Evaluate the Integral	integral of 28/((4x+3)^8) with respect to x	$\int \frac{28}{{(4 x + 3)}^{8}} d x$
28024	Evaluate the Integral	integral of (2a)/( square root of x)-b/(x^2)+3c cube root of x^2 with respect to x	$\int \frac{2 a}{\sqrt{x}} - \frac{b}{x^{2}} + 3 c \sqrt[3]{x^{2}} d x$
28025	Evaluate the Integral	integral of (28t^3)/( square root of 3-t^4) with respect to tdx	$\int \frac{28 t^{3}}{\sqrt{3 - t^{4}}} d t d x$
28026	Evaluate the Integral	integral of 28/((7x+3)^5) with respect to x	$\int \frac{28}{{(7 x + 3)}^{5}} d x$
28027	Evaluate the Integral	integral of (2x+7)/((5x^2+35x)^9) with respect to x	$\int \frac{2 x + 7}{{(5 x^{2} + 35 x)}^{9}} d x$
28028	Evaluate the Integral	integral of (2x-1)/(x(x-1)) with respect to x	$\int \frac{2 x - 1}{x (x - 1)} d x$
28029	Evaluate the Integral	integral of (2x+4)/(x^3-2x^2) with respect to x	$\int \frac{2 x + 4}{x^{3} - 2 x^{2}} d x$
28030	Evaluate the Integral	integral of (2x)/(1-x^2) with respect to x	$\int \frac{2 x}{1 - x^{2}} d x$
28031	Evaluate the Integral	integral of (2x+1)/(x^2-7x+12) with respect to x	$\int \frac{2 x + 1}{x^{2} - 7 x + 12} d x$
28032	Evaluate the Integral	integral of (3x)/(x^2+10) with respect to x	$\int \frac{3 x}{x^{2} + 10} d x$
28033	Evaluate the Integral	integral of (3x)/(1+9x^2) with respect to x	$\int \frac{3 x}{1 + 9 x^{2}} d x$
28034	Evaluate the Integral	integral of (36-4x^2)/9 with respect to x	$\int \frac{36 - 4 x^{2}}{9} d x$
28035	Evaluate the Integral	integral of 3/(x-1) with respect to x	$\int \frac{3}{x - 1} d x$
28036	Evaluate the Integral	integral of (3t)/( cube root of t^2+3) with respect to t	$\int \frac{3 t}{\sqrt[3]{t^{2} + 3}} d t$
28037	Evaluate the Integral	integral of (3x)/( cube root of x^2+5) with respect to x	$\int \frac{3 x}{\sqrt[3]{x^{2} + 5}} d x$
28038	Evaluate the Integral	integral from (3pi)/2 to 2pi of cos(x) with respect to x	$\int_{\frac{3 π}{2}}^{2 π} \cos (x) d x$
28039	Evaluate the Integral	integral of (3tan(x)-4cos(x)^2)/(cos(x)) with respect to x	$\int \frac{3 \tan (x) - 4 \cos^{2} (x)}{\cos (x)} d x$
28040	Evaluate the Integral	integral of (3u-3)/((u^2-2u+6)^2) with respect to u	$\int \frac{3 u - 3}{{(u^{2} - 2 u + 6)}^{2}} d u$
28041	Evaluate the Integral	integral of 35/(x^2) with respect to x	$\int \frac{35}{x^{2}} d x$
28042	Evaluate the Integral	integral of (3x)/(x^2-3x-4) with respect to x	$\int \frac{3 x}{x^{2} - 3 x - 4} d x$
28043	Evaluate the Integral	integral of (4x^2)/( square root of x^3+8) with respect to x	$\int \frac{4 x^{2}}{\sqrt{x^{3} + 8}} d x$
28044	Evaluate the Integral	integral of (4x^2)/( square root of 7-8x^3) with respect to x	$\int \frac{4 x^{2}}{\sqrt{7 - 8 x^{3}}} d x$
28045	Evaluate the Integral	integral of (4x^2+38x+9)/((x+3)^2(x+5)) with respect to x	$\int \frac{4 x^{2} + 38 x + 9}{{(x + 3)}^{2} (x + 5)} d x$
28046	Evaluate the Integral	integral of (30x^5)/(4+5x^6) with respect to x	$\int \frac{30 x^{5}}{4 + 5 x^{6}} d x$
28047	Evaluate the Integral	integral of 3/(4x-1) with respect to x	$\int \frac{3}{4 x - 1} d x$
28048	Evaluate the Integral	integral of 3/(2x+1) with respect to x	$\int \frac{3}{2 x + 1} d x$
28049	Evaluate the Integral	integral of 3/2*(xe^(-6x)) with respect to x	$\int \frac{3}{2} \cdot (x e^{- 6 x}) d x$
28050	Evaluate the Integral	integral of 2/( square root of 7-6x-x^2) with respect to x	$\int \frac{2}{\sqrt{7 - 6 x - x^{2}}} d x$
28051	Evaluate the Integral	integral of (2x^2-12x+4)/(x^3-4x^2) with respect to x	$\int \frac{2 x^{2} - 12 x + 4}{x^{3} - 4 x^{2}} d x$
28052	Evaluate the Integral	integral of (2x^2-3x+1)/(3x-3) with respect to x	$\int \frac{2 x^{2} - 3 x + 1}{3 x - 3} d x$
28053	Evaluate the Integral	integral of (2x^2-5x+2)/(x^3+x) with respect to x	$\int \frac{2 x^{2} - 5 x + 2}{x^{3} + x} d x$
28054	Evaluate the Integral	integral of (2x^3-1)/(x^3) with respect to x	$\int \frac{2 x^{3} - 1}{x^{3}} d x$
28055	Evaluate the Integral	integral of (2x^3-4x^2-15x+5)/(x^2-2x-8) with respect to x	$\int \frac{2 x^{3} - 4 x^{2} - 15 x + 5}{x^{2} - 2 x - 8} d x$
28056	Evaluate from the Right	limit as x approaches 0 of natural log of x	$lim_{x \to 0} \ln (x)$
28057	Evaluate the Integral	integral of (20x^3)/(4+5x^4) with respect to x	$\int \frac{20 x^{3}}{4 + 5 x^{4}} d x$
28058	Evaluate the Integral	integral of (20x^5-20x^4+x)/x with respect to x	$\int \frac{20 x^{5} - 20 x^{4} + x}{x} d x$
28059	Evaluate the Integral	integral of 20/((4x+5)^6) with respect to x	$\int \frac{20}{{(4 x + 5)}^{6}} d x$
28060	Evaluate the Integral	integral of 2^((-x)/2) with respect to x	$\int 2^{\frac{- x}{2}} d x$
28061	Evaluate the Integral	integral of (24x^5)/(3+4x^6) with respect to x	$\int \frac{24 x^{5}}{3 + 4 x^{6}} d x$
28062	Evaluate the Integral	integral of 25/(x natural log of 6x) with respect to x	$\int \frac{25}{x \ln (6 x)} d x$
28063	Evaluate the Integral	integral of 25/(x natural log of 9x) with respect to x	$\int \frac{25}{x \ln (9 x)} d x$
28064	Evaluate the Integral	integral of 24/((4x+9)^7) with respect to x	$\int \frac{24}{{(4 x + 9)}^{7}} d x$
28065	Evaluate the Integral	integral of 2/(50+t) with respect to t	$\int \frac{2}{50 + t} d t$
28066	Evaluate the Integral	integral of 2/x-1/(x^2) with respect to x	$\int \frac{2}{x} - \frac{1}{x^{2}} d x$
28067	Evaluate the Integral	integral of 2/(3x^4) with respect to x	$\int \frac{2}{3 x^{4}} d x$
28068	Evaluate the Integral	integral of 2/(3x+5) with respect to x	$\int \frac{2}{3 x + 5} d x$
28069	Evaluate the Integral	integral of 2/(4+x^2) with respect to x	$\int \frac{2}{4 + x^{2}} d x$
28070	Evaluate the Integral	integral of (16x+48)/((x^2+6x+4)^9) with respect to x	$\int \frac{16 x + 48}{{(x^{2} + 6 x + 4)}^{9}} d x$
28071	Evaluate the Integral	integral of 17/x with respect to x	$\int \frac{17}{x} d x$
28072	Evaluate the Integral	integral of 18/x with respect to x	$\int \frac{18}{x} d x$
28073	Evaluate the Integral	integral of (1-tan(x))/(1+tan(x)) with respect to x	$\int \frac{1 - \tan (x)}{1 + \tan (x)} d x$
28074	Evaluate the Integral	integral of (18x^5)/(2+3x^6) with respect to x	$\int \frac{18 x^{5}}{2 + 3 x^{6}} d x$
28075	Evaluate the Integral	integral of (2x^2)/(x^2+9) with respect to x	$\int \frac{2 x^{2}}{x^{2} + 9} d x$
28076	Evaluate the Integral	integral of (-1200x)/( square root of 25-x^2) with respect to x	$\int \frac{- 1200 x}{\sqrt{25 - x^{2}}} d x$
28077	Evaluate the Integral	integral of (12+10x-2x^2)/(x^3-4x) with respect to x	$\int \frac{12 + 10 x - 2 x^{2}}{x^{3} - 4 x} d x$
28078	Evaluate the Integral	integral of 12x^(1/2) with respect to x	$\int 12 x^{\frac{1}{2}} d x$
28079	Evaluate the Integral	integral of (1-3y)/( square root of 2y-3y^2) with respect to y	$\int \frac{1 - 3 y}{\sqrt{2 y - 3 y^{2}}} d y$
28080	Evaluate the Integral	integral of 13/(100-7x) with respect to x	$\int \frac{13}{100 - 7 x} d x$
28081	Evaluate the Integral	integral of 13/(x natural log of 8x) with respect to x	$\int \frac{13}{x \ln (8 x)} d x$
28082	Evaluate the Integral	integral of (14x)/( square root of 7x^2+2) with respect to x	$\int \frac{14 x}{\sqrt{7 x^{2} + 2}} d x$
28083	Evaluate the Integral	integral of (10y^2)/(5+y^3) with respect to y	$\int \frac{10 y^{2}}{5 + y^{3}} d y$
28084	Evaluate the Integral	integral of 10/(10x-1) with respect to x	$\int \frac{10}{10 x - 1} d x$
28085	Evaluate the Integral	integral of (1+6t^5)/(11t) with respect to t	$\int \frac{1 + 6 t^{5}}{11 t} d t$
28086	Evaluate the Integral	integral of (1+2t^3)/(4t) with respect to t	$\int \frac{1 + 2 t^{3}}{4 t} d t$
28087	Evaluate the Integral	integral of (1+2t^3)/(7t) with respect to t	$\int \frac{1 + 2 t^{3}}{7 t} d t$
28088	Evaluate the Integral	integral of (1+6t^5)/(7t) with respect to t	$\int \frac{1 + 6 t^{5}}{7 t} d t$
28089	Evaluate the Integral	integral of (1+6t^7)/(7t) with respect to t	$\int \frac{1 + 6 t^{7}}{7 t} d t$
28090	Evaluate the Integral	integral of (10x)/(2+5x^2) with respect to x	$\int \frac{10 x}{2 + 5 x^{2}} d x$
28091	Evaluate the Integral	integral of (11x+17)/(2x^2+7x-4) with respect to x	$\int \frac{11 x + 17}{2 x^{2} + 7 x - 4} d x$
28092	Evaluate the Integral	integral of 10x^(3/2) with respect to x	$\int 10 x^{\frac{3}{2}} d x$
28093	Evaluate the Integral	integral of (12x^5)/(3+2x^6) with respect to x	$\int \frac{12 x^{5}}{3 + 2 x^{6}} d x$
28094	Evaluate the Integral	integral of 10^(2x) with respect to x	$\int 10^{2 x} d x$
28095	Evaluate the Integral	integral of (10x)/( square root of x^2+25) with respect to x	$\int \frac{10 x}{\sqrt{x^{2} + 25}} d x$
28096	Evaluate the Integral	integral of (10+u)/u with respect to u	$\int \frac{10 + u}{u} d u$
28097	Evaluate the Integral	integral of 10^(3x) with respect to x	$\int 10^{3 x} d x$
28098	Evaluate the Integral	integral of -1000/(x^2) with respect to x	$\int - \frac{1000}{x^{2}} d x$
28099	Evaluate the Integral	integral of 9/(8+9x) with respect to x	$\int \frac{9}{8 + 9 x} d x$
28100	Evaluate the Integral	integral of 9/x-2e^(3x)+ square root of x^5 with respect to x	$\int \frac{9}{x} - 2 e^{3 x} + \sqrt{x^{5}} d x$