Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
8701	Evaluate the Integral	integral of x^(7/3) with respect to x	$\int x^{\frac{7}{3}} d x$
8702	Evaluate the Integral	integral of x^15 with respect to x	$\int x^{15} d x$
8703	Evaluate the Integral	integral of x^10 natural log of x with respect to x	$\int x^{10} \ln (x) d x$
8704	Evaluate the Integral	integral of x/(x-2) with respect to x	$\int \frac{x}{x - 2} d x$
8705	Evaluate the Integral	integral of x/(x-5) with respect to x	$\int \frac{x}{x - 5} d x$
8706	Evaluate the Integral	integral of x^(3/2) natural log of x with respect to x	$\int x^{\frac{3}{2}} \ln (x) d x$
8707	Evaluate the Integral	integral of x^(1/6) with respect to x	$\int x^{\frac{1}{6}} d x$
8708	Evaluate the Integral	integral of x/(16x^4-1) with respect to x	$\int \frac{x}{16 x^{4} - 1} d x$
8709	Evaluate the Integral	integral of x/(1-x) with respect to x	$\int \frac{x}{1 - x} d x$
8710	Evaluate the Integral	integral of x/(2x^2-3) with respect to x	$\int \frac{x}{2 x^{2} - 3} d x$
8711	Evaluate the Integral	integral of x/(4+x^2) with respect to x	$\int \frac{x}{4 + x^{2}} d x$
8712	Evaluate the Integral	integral of x^2(x^3+1)^4 with respect to x	$\int x^{2} {(x^{3} + 1)}^{4} d x$
8713	Evaluate the Integral	integral of x^2 with respect to y	$\int x^{2} d y$
8714	Evaluate the Integral	integral of x^2e^(11x) with respect to x	$\int x^{2} e^{11 x} d x$
8715	Evaluate the Integral	integral of x^2e^(4x^3) with respect to x	$\int x^{2} e^{4 x^{3}} d x$
8716	Evaluate the Integral	integral of x^2cos(4x) with respect to x	$\int x^{2} \cos (4 x) d x$
8717	Evaluate the Integral	integral of x^2cos(2x) with respect to x	$\int x^{2} \cos (2 x) d x$
8718	Evaluate the Integral	integral of x^2 square root of 1-x^2 with respect to x	$\int x^{2} \sqrt{1 - x^{2}} d x$
8719	Evaluate the Integral	integral of x/((1+x^2)^(1/2)) with respect to x	$\int \frac{x}{{(1 + x^{2})}^{\frac{1}{2}}} d x$
8720	Evaluate the Integral	integral of x/((1-2x^2)^3) with respect to x	$\int \frac{x}{{(1 - 2 x^{2})}^{3}} d x$
8721	Find the Critical Points	f(x)=x^8-8x^7	$f (x) = x^{8} - 8 x^{7}$
8722	Evaluate the Integral	integral of cube root of 5-3x^2(-6x) with respect to x	$\int \sqrt[3]{5 - 3 x^{2}} (- 6 x) d x$
8723	Evaluate the Integral	integral of fourth root of x^3+1 with respect to x	$\int \sqrt[4]{x^{3} + 1} d x$
8724	Evaluate the Integral	integral of square root of 8x+7 with respect to x	$\int \sqrt{8 x + 7} d x$
8725	Evaluate the Integral	integral of square root of cos(x) with respect to x	$\int \sqrt{\cos (x)} d x$
8726	Evaluate the Integral	integral of square root of sin(x)cos(x) with respect to x	$\int \sqrt{\sin (x)} \cos (x) d x$
8727	Evaluate the Integral	integral of square root of xe^( square root of x) with respect to x	$\int \sqrt{x} e^{\sqrt{x}} d x$
8728	Evaluate the Integral	integral of square root of xsin(1+x^(3/2)) with respect to x	$\int \sqrt{x} \sin (1 + x^{\frac{3}{2}}) d x$
8729	Evaluate the Integral	integral of e^(9x) with respect to x	$\int e^{9 x} d x$
8730	Evaluate the Integral	integral of square root of 2-3x with respect to x	$\int \sqrt{2 - 3 x} d x$
8731	Evaluate the Integral	integral of square root of 3-2x-x^2 with respect to x	$\int \sqrt{3 - 2 x - x^{2}} d x$
8732	Evaluate the Integral	integral of square root of 49-x^2 with respect to x	$\int \sqrt{49 - x^{2}} d x$
8733	Evaluate the Integral	integral of square root of 6x-7 with respect to x	$\int \sqrt{6 x - 7} d x$
8734	Evaluate the Integral	integral of x^3 square root of 1-x^2 with respect to x	$\int x^{3} \sqrt{1 - x^{2}} d x$
8735	Evaluate the Integral	integral of x^2sin(4x) with respect to x	$\int x^{2} \sin (4 x) d x$
8736	Evaluate the Integral	integral of x^2sin(5x) with respect to x	$\int x^{2} \sin (5 x) d x$
8737	Evaluate the Integral	integral of x^4e^(-x) with respect to x	$\int x^{4} e^{- x} d x$
8738	Evaluate the Integral	integral of x^4 square root of x^5+5 with respect to x	$\int x^{4} \sqrt{x^{5} + 5} d x$
8739	Evaluate the Integral	integral of x^4e^(-2x) with respect to x	$\int x^{4} e^{- 2 x} d x$
8740	Evaluate the Integral	integral of x^4-2x^3 with respect to x	$\int x^{4} - 2 x^{3} d x$
8741	Evaluate the Integral	integral of x^3sin(x^2) with respect to x	$\int x^{3} \sin (x^{2}) d x$
8742	Evaluate the Integral	integral of x^3sin(x^4) with respect to x	$\int x^{3} \sin (x^{4}) d x$
8743	Evaluate the Integral	integral of xa^x with respect to x	$\int x a^{x} d x$
8744	Evaluate the Integral	integral of (x+2)/(x^2+4x+5) with respect to x	$\int \frac{x + 2}{x^{2} + 4 x + 5} d x$
8745	Evaluate the Integral	integral of (x+4)/(x^2+5x-6) with respect to x	$\int \frac{x + 4}{x^{2} + 5 x - 6} d x$
8746	Evaluate the Integral	integral of x^5sin(x^6) with respect to x	$\int x^{5} \sin (x^{6}) d x$
8747	Evaluate the Integral	integral of (x+1)/(x^2+2x+19) with respect to x	$\int \frac{x + 1}{x^{2} + 2 x + 19} d x$
8748	Evaluate the Integral	integral from 0 to pi/2 of sin(x)cos(x) with respect to x	$\int_{0}^{\frac{π}{2}} \sin (x) \cos (x) d x$
8749	Evaluate the Integral	integral from 0 to pi/2 of xsin(x^2) with respect to x	$\int_{0}^{\frac{π}{2}} x \sin (x^{2}) d x$
8750	Evaluate the Integral	integral from 0 to pi/3 of (cos(x)+sec(x))^2 with respect to x	$\int_{0}^{\frac{π}{3}} {(\cos (x) + \sec (x))}^{2} d x$
8751	Evaluate the Integral	integral from 0 to pi/2 of xcos(2x) with respect to x	$\int_{0}^{\frac{π}{2}} x \cos (2 x) d x$
8752	Evaluate the Integral	integral from 0 to pi/2 of xcos(x) with respect to x	$\int_{0}^{\frac{π}{2}} x \cos (x) d x$
8753	Evaluate the Integral	integral from 0 to pi/2 of sin(x)^4 with respect to x	$\int_{0}^{\frac{π}{2}} \sin^{4} (x) d x$
8754	Evaluate the Integral	integral from 0 to pi/2 of 2sin(x)^2cos(x) with respect to x	$\int_{0}^{\frac{π}{2}} 2 \sin^{2} (x) \cos (x) d x$
8755	Evaluate the Integral	integral from 0 to pi/2 of sin(x)^7cos(x)^5 with respect to x	$\int_{0}^{\frac{π}{2}} \sin^{7} (x) \cos^{5} (x) d x$
8756	Evaluate the Integral	integral from 0 to pi/2 of cos(x)^2sin(x) with respect to x	$\int_{0}^{\frac{π}{2}} \cos^{2} (x) \sin (x) d x$
8757	Evaluate the Integral	integral from 0 to pi/2 of (cos(t))/( square root of 1+sin(t)^2) with respect to t	$\int_{0}^{\frac{π}{2}} \frac{\cos (t)}{\sqrt{1 + \sin^{2} (t)}} d t$
8758	Evaluate the Integral	integral from 0 to pi/2 of e^(-cos(x))sin(x) with respect to x	$\int_{0}^{\frac{π}{2}} e^{- \cos (x)} \sin (x) d x$
8759	Evaluate the Integral	integral from 0 to pi/2 of r/(4+r^2) with respect to r	$\int_{0}^{\frac{π}{2}} \frac{r}{4 + r^{2}} d r$
8760	Evaluate the Integral	integral from 0 to pi/2 of sec(x/2)^2 with respect to x	$\int_{0}^{\frac{π}{2}} \sec^{2} (\frac{x}{2}) d x$
8761	Evaluate the Integral	integral from 0 to pi/12 of 1-cos(2x) with respect to x	$\int_{0}^{\frac{π}{12}} 1 - \cos (2 x) d x$
8762	Evaluate the Integral	integral from 0 to pi/2 of sin(x)^6(x) with respect to x	$\int_{0}^{\frac{π}{2}} \sin^{6} (x) (x) d x$
8763	Evaluate the Integral	integral of y^2(1+y)^2 with respect to y	$\int y^{2} {(1 + y)}^{2} d y$
8764	Evaluate the Integral	integral of (y-2)/(y+3) with respect to y	$\int \frac{y - 2}{y + 3} d y$
8765	Evaluate the Integral	integral from 0 to 1/2 of 1/( square root of 1-x^2) with respect to x	$\int_{0}^{\frac{1}{2}} \frac{1}{\sqrt{1 - x^{2}}} d x$
8766	Evaluate the Integral	integral from 0 to 1/2 of 1/( square root of 1-x^2) with respect to xdx	$\int_{0}^{\frac{1}{2}} \frac{1}{\sqrt{1 - x^{2}}} d x d x$
8767	Evaluate the Integral	integral from 0 to 1/2 of cos(pix) with respect to x	$\int_{0}^{\frac{1}{2}} \cos (π x) d x$
8768	Evaluate the Integral	integral from 0 to 1/8 of (arcsin(4x))/( square root of 1-16x^2) with respect to x	$\int_{0}^{\frac{1}{8}} \frac{\arcsin (4 x)}{\sqrt{1 - 16 x^{2}}} d x$
8769	Evaluate the Integral	integral from 0 to 1/6 of 3/( square root of 1-9x^2) with respect to x	$\int_{0}^{\frac{1}{6}} \frac{3}{\sqrt{1 - 9 x^{2}}} d x$
8770	Evaluate the Integral	integral from 3 to 5 of 1/( square root of x)-4 with respect to x	$\int_{3}^{5} \frac{1}{\sqrt{x}} - 4 d x$
8771	Evaluate the Integral	integral from 3 to 5 of xcos(x) with respect to x	$\int_{3}^{5} x \cos (x) d x$
8772	Evaluate the Integral	integral of 3e^(-2x) with respect to x	$\int 3 e^{- 2 x} d x$
8773	Evaluate the Integral	integral of 3cos(x)^2 with respect to x	$\int 3 \cos^{2} (x) d x$
8774	Evaluate the Integral	integral of 3t^6 with respect to t	$\int 3 t^{6} d t$
8775	Evaluate the Integral	integral of 3te^(-t^2) with respect to t	$\int 3 t e^{- t^{2}} d t$
8776	Evaluate the Integral	integral of -3e^(-3x) with respect to x	$\int - 3 e^{- 3 x} d x$
8777	Evaluate the Integral	integral of 3e^(6x) with respect to x	$\int 3 e^{6 x} d x$
8778	Evaluate the Integral	integral of (3(sin(2x)))/(sin(x)) with respect to x	$\int \frac{3 (\sin (2 x))}{\sin (x)} d x$
8779	Evaluate the Integral	integral from 3 to 9 of ydx with respect to x	$\int_{3}^{9} yds x d x$
8780	Evaluate the Integral	integral from 3 to 6 of 2x square root of x^2-4 with respect to x	$\int_{3}^{6} 2 x \sqrt{x^{2} - 4} d x$
8781	Evaluate the Integral	integral of 3x^2e^x with respect to x	$\int 3 x^{2} e^{x} d x$
8782	Evaluate the Integral	integral of 3x^2sin(x) with respect to x	$\int 3 x^{2} \sin (x) d x$
8783	Evaluate the Integral	integral of 3xe^(0.5x^2) with respect to x	$\int 3 x e^{0.5 x^{2}} d x$
8784	Evaluate the Integral	integral of 3xe^(8x) with respect to x	$\int 3 x e^{8 x} d x$
8785	Evaluate the Integral	integral of 36-x^2 with respect to x	$\int 36 - x^{2} d x$
8786	Evaluate the Integral	integral from 36 to 49 of ( natural log of y)/( square root of y) with respect to y	$\int_{36}^{49} \frac{\ln (y)}{\sqrt{y}} d y$
8787	Evaluate the Integral	integral of 3-3x with respect to x	$\int 3 - 3 x d x$
8788	Evaluate the Integral	integral of 3cos(2x) with respect to x	$\int 3 \cos (2 x) d x$
8789	Evaluate the Integral	integral of 30t^5e^(-t^6) with respect to t	$\int 30 t^{5} e^{- t^{6}} d t$
8790	Evaluate the Integral	integral of 3sec(x)tan(x) with respect to x	$\int 3 \sec (x) \tan (x) d x$
8791	Evaluate the Integral	integral of 3sin(2x) with respect to x	$\int 3 \sin (2 x) d x$
8792	Evaluate the Integral	integral of 3x+4 with respect to x	$\int 3 x + 4 d x$
8793	Evaluate the Integral	integral of 3ydy with respect to y	$\int 3 yds y d y$
8794	Evaluate the Integral	integral from -4 to 3 of (5-x^2)-(x-7) with respect to x	$\int_{- 4}^{3} (5 - x^{2}) - (x - 7) d x$
8795	Evaluate the Integral	integral of 2x^3e^(-x^2) with respect to x	$\int 2 x^{3} e^{- x^{2}} d x$
8796	Evaluate the Integral	integral of -2xe^(-x^2) with respect to x	$\int - 2 x e^{- x^{2}} d x$
8797	Evaluate the Integral	integral from 2 square root of 2 to 4 of 1/(t^3 square root of t^2-4) with respect to t	$\int_{2 \sqrt{2}}^{4} \frac{1}{t^{3} \sqrt{t^{2} - 4}} d t$
8798	Evaluate the Integral	integral of -2sec(x)^2 with respect to x	$\int - 2 \sec^{2} (x) d x$
8799	Evaluate the Integral	integral of 2t^-8 with respect to t	$\int 2 t^{- 8} d t$
8800	Evaluate the Integral	integral of 2e^(9x) with respect to x	$\int 2 e^{9 x} d x$