Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
2801	Evaluate the Integral	integral of x/( square root of 2x-1) with respect to x	$\int \frac{x}{\sqrt{2 x - 1}} d x$
2802	Evaluate the Integral	integral of x^2 square root of 1+x^3 with respect to x	$\int x^{2} \sqrt{1 + x^{3}} d x$
2803	Evaluate the Integral	integral of x^2 natural log of 3x with respect to x	$\int x^{2} \ln (3 x) d x$
2804	Evaluate the Integral	integral of x^2(x^3-1)^4 with respect to x	$\int x^{2} {(x^{3} - 1)}^{4} d x$
2805	Evaluate the Integral	integral of x^2*e^x with respect to x	$\int x^{2} \cdot e^{x} d x$
2806	Evaluate the Integral	integral of x^2*e^(-x) with respect to x	$\int x^{2} \cdot e^{- x} d x$
2807	Evaluate the Integral	integral of x/(x^2-4) with respect to x	$\int \frac{x}{x^{2} - 4} d x$
2808	Evaluate the Integral	integral of x^11 natural log of x with respect to x	$\int x^{11} \ln (x) d x$
2809	Evaluate the Integral	integral of x^(5/2) with respect to x	$\int x^{\frac{5}{2}} d x$
2810	Evaluate the Integral	integral of e^(-6x) with respect to x	$\int e^{- 6 x} d x$
2811	Find the Derivative - d/d@VAR	f(x) = sixth root of x	$f (x) = \sqrt[6]{x}$
2812	Evaluate the Integral	integral of e^x*cos(x) with respect to x	$\int e^{x} \cdot \cos (x) d x$
2813	Evaluate the Integral	integral of ( natural log of x)/(x^5) with respect to x	$\int \frac{\ln (x)}{x^{5}} d x$
2814	Evaluate the Integral	integral of e^(-2t) with respect to t	$\int e^{- 2 t} d t$
2815	Evaluate the Integral	integral of e^((x^2)/2) with respect to x	$\int e^{\frac{x^{2}}{2}} d x$
2816	Evaluate the Integral	integral of csc(3x)^2 with respect to x	$\int \csc^{2} (3 x) d x$
2817	Evaluate the Integral	integral of sin(x)^4cos(x)^3 with respect to x	$\int \sin^{4} (x) \cos^{3} (x) d x$
2818	Evaluate the Integral	integral of square root of x^2+4 with respect to x	$\int \sqrt{x^{2} + 4} d x$
2819	Evaluate the Integral	integral of te^(t^2) with respect to t	$\int t e^{t^{2}} d t$
2820	Evaluate the Integral	integral of square root of x^11 with respect to x	$\int \sqrt{x^{11}} d x$
2821	Evaluate the Integral	integral of sec(x)^6 with respect to x	$\int \sec^{6} (x) d x$
2822	Evaluate the Integral	integral of (sec(x))/(tan(x)) with respect to x	$\int \frac{\sec (x)}{\tan (x)} d x$
2823	Evaluate the Integral	integral of 3/(x^3) with respect to x	$\int \frac{3}{x^{3}} d x$
2824	Evaluate the Integral	integral of 2/(x^2+1) with respect to x	$\int \frac{2}{x^{2} + 1} d x$
2825	Evaluate the Integral	integral of 2/(x-2) with respect to x	$\int \frac{2}{x - 2} d x$
2826	Evaluate the Integral	integral of (1-cos(2x))/2 with respect to x	$\int \frac{1 - \cos (2 x)}{2} d x$
2827	Evaluate the Integral	integral of cos(x)^2tan(x)^3 with respect to x	$\int \cos^{2} (x) \tan^{3} (x) d x$
2828	Evaluate the Integral	integral of (x^4)/(x-1) with respect to x	$\int \frac{x^{4}}{x - 1} d x$
2829	Evaluate the Integral	integral of (x^4-3x^2+5)/(x^4) with respect to x	$\int \frac{x^{4} - 3 x^{2} + 5}{x^{4}} d x$
2830	Evaluate the Integral	integral of (x^9)/(1+x^20) with respect to x	$\int \frac{x^{9}}{1 + x^{20}} d x$
2831	Evaluate the Integral	integral of (x^2)/(4+x^2) with respect to x	$\int \frac{x^{2}}{4 + x^{2}} d x$
2832	Evaluate the Integral	integral of 1/( square root of 8x) with respect to x	$\int \frac{1}{\sqrt{8 x}} d x$
2833	Evaluate the Integral	integral of 1/( square root of 1-9x^2) with respect to x	$\int \frac{1}{\sqrt{1 - 9 x^{2}}} d x$
2834	Evaluate the Integral	integral of 1/( square root of 4+x^2) with respect to x	$\int \frac{1}{\sqrt{4 + x^{2}}} d x$
2835	Evaluate the Integral	integral of 1/( square root of x^2-25) with respect to x	$\int \frac{1}{\sqrt{x^{2} - 25}} d x$
2836	Evaluate the Integral	integral of 1/(x^13) with respect to x	$\int \frac{1}{x^{13}} d x$
2837	Evaluate the Limit	limit as x approaches 1 of (x^4-1)/(x-1)	$lim_{x \to 1} \frac{x^{4} - 1}{x - 1}$
2838	Evaluate the Integral	integral of 1/(x square root of x^2-4) with respect to x	$\int \frac{1}{x \sqrt{x^{2} - 4}} d x$
2839	Evaluate the Integral	integral of 1/(2x+5) with respect to x	$\int \frac{1}{2 x + 5} d x$
2840	Evaluate the Integral	integral of 1/(2y) with respect to y	$\int \frac{1}{2 y} d y$
2841	Evaluate the Integral	integral of 1/(2x-1) with respect to x	$\int \frac{1}{2 x - 1} d x$
2842	Evaluate the Integral	integral of 1/2x with respect to x	$\int \frac{1}{2} x d x$
2843	Evaluate the Integral	integral of 1/5*sin(5x) with respect to x	$\int \frac{1}{5} \cdot \sin (5 x) d x$
2844	Evaluate the Integral	integral of 1/(3x+5) with respect to x	$\int \frac{1}{3 x + 5} d x$
2845	Evaluate the Integral	integral of 1/(3x-2) with respect to x	$\int \frac{1}{3 x - 2} d x$
2846	Evaluate the Integral	integral of 1/(4x^6) with respect to x	$\int \frac{1}{4 x^{6}} d x$
2847	Find the 2nd Derivative	sin(x)+cos(x)	$\sin (x) + \cos (x)$
2848	Find the 2nd Derivative	y = square root of x^2+1	$y = \sqrt{x^{2} + 1}$
2849	Evaluate the Integral	integral of 3x^8-7x^3+7 with respect to x	$\int 3 x^{8} - 7 x^{3} + 7 d x$
2850	Evaluate the Integral	integral of 2x-7 with respect to x	$\int 2 x - 7 d x$
2851	Evaluate the Integral	integral of (1+3t)t^2 with respect to t	$\int (1 + 3 t) t^{2} d t$
2852	Evaluate the Integral	integral of 5e^z+4 with respect to z	$\int 5 e^{z} + 4 d z$
2853	Evaluate the Integral	integral of 4x-5 with respect to x	$\int 4 x - 5 d x$
2854	Find the 4th Derivative	f(x)=sin(x)	$f (x) = \sin (x)$
2855	Evaluate the Integral	integral of 12/( square root of x)+12 square root of x with respect to x	$\int \frac{12}{\sqrt{x}} + 12 \sqrt{x} d x$
2856	Evaluate the Integral	integral of x^2-7x+3 with respect to x	$\int x^{2} - 7 x + 3 d x$
2857	Evaluate the Integral	integral of (1-2x)^9 with respect to x	$\int {(1 - 2 x)}^{9} d x$
2858	Evaluate the Integral	integral of ( natural log of (x)^6)/x with respect to x	$\int \frac{\ln ({(x)}^{6})}{x} d x$
2859	Evaluate the Integral	integral of ( natural log of (x)^4)/x with respect to x	$\int \frac{\ln ({(x)}^{4})}{x} d x$
2860	Evaluate the Integral	integral of (e^(2x))/(1+e^(2x)) with respect to x	$\int \frac{e^{2 x}}{1 + e^{2 x}} d x$
2861	Evaluate the Integral	integral of sin(x)^4 with respect to x	$\int \sin^{4} (x) d x$
2862	Evaluate Using L'Hospital's Rule	limit as x approaches 8 of ( natural log of x)/( square root of x)	$lim_{x \to 8} \frac{\ln (x)}{\sqrt{x}}$
2863	Evaluate Using L'Hospital's Rule	limit as x approaches pi/2 of (cos(x))/(1-sin(x))	$lim_{x \to \frac{π}{2}} \frac{\cos (x)}{1 - \sin (x)}$
2864	Evaluate the Summation	sum from k=5 to 26 of 4	$\sum_{k = 5}^{26} 4$
2865	Evaluate the Summation	sum from n=1 to 14 of 3n+2	$\sum_{n = 1}^{14} 3 n + 2$
2866	Evaluate the Summation	sum from n=1 to 8 of 1/n	$\sum_{n = 1}^{8} \frac{1}{n}$
2867	Evaluate the Summation	sum from n=1 to 8 of -4(1/3)^(n-1)	$\sum_{n = 1}^{8} - 4 {(\frac{1}{3})}^{n - 1}$
2868	Evaluate the Summation	sum from i=5 to 13 of 3i+2	$\sum_{i = 5}^{13} 3 i + 2$
2869	Evaluate the Summation	sum from i=1 to 10 of i(i^2+1)	$\sum_{i = 1}^{10} i (i^{2} + 1)$
2870	Find the 2nd Derivative	y = square root of x+11	$y = \sqrt{x + 11}$
2871	Find the 2nd Derivative	-x/y	$- \frac{x}{y}$
2872	Find the 2nd Derivative	sec(x)^2	$\sec^{2} (x)$
2873	Find the Derivative - d/dx	natural log of tan(x)	$\ln (\tan (x))$
2874	Find the Derivative - d/dx	y=cos(x^2)	$y = \cos (x^{2})$
2875	Find the Derivative - d/dx	square root of x^7	$\sqrt{x^{7}}$
2876	Find the Derivative - d/dx	cos(x)^9	$\cos^{9} (x)$
2877	Find the Derivative - d/dx	y=8	$y = 8$
2878	Find the Derivative - d/dx	(2x-7)^4(x^2+x+1)^5	${(2 x - 7)}^{4} {(x^{2} + x + 1)}^{5}$
2879	Find the Derivative - d/dx	cos(2x)^2	$\cos^{2} (2 x)$
2880	Find the Derivative - d/dx	9/x	$\frac{9}{x}$
2881	Find the Derivative - d/dx	natural log of x^5	$\ln (x^{5})$
2882	Find the Derivative - d/dX	x^2e^(3x)	$x^{2} e^{3 x}$
2883	Find the Derivative - d/dx	1/2*(xe^(-1/2x))	$\frac{1}{2} \cdot (x e^{\frac{- 1}{2} x})$
2884	Find the Derivative - d/dx	y=4x^2-5x	$y = 4 x^{2} - 5 x$
2885	Evaluate the Integral	integral of cube root of x^11 with respect to x	$\int \sqrt[3]{x^{11}} d x$
2886	Evaluate the Limit	limit as x approaches 0 of tan(x)	$lim_{x \to 0} \tan (x)$
2887	Evaluate the Limit	limit as x approaches pi of sin(x-sin(x))	$lim_{x \to π} \sin (x - \sin (x))$
2888	Evaluate the Limit	( limit as x approaches 0 of 2(x+h)-2x)/h	$\frac{lim_{x \to 0} 2 (x + h) - 2 x}{h}$
2889	Find the Derivative - d/dt	cos(2t)	$\cos (2 t)$
2890	Evaluate the Integral	integral of 1/( square root of 4-9x^2) with respect to x	$\int \frac{1}{\sqrt{4 - 9 x^{2}}} d x$
2891	Evaluate the Limit	limit as x approaches 0 of (1/(2+x)-1/2)/x	$lim_{x \to 0} \frac{\frac{1}{2 + x} - \frac{1}{2}}{x}$
2892	Evaluate the Limit	limit as x approaches 8 of square root of x	$lim_{x \to 8} \sqrt{x}$
2893	Evaluate the Limit	limit as x approaches infinity of 1/x	$lim_{x \to \infty} \frac{1}{x}$
2894	Evaluate the Limit	limit as x approaches 8 of (1-4/x)^x	$lim_{x \to 8} {(1 - \frac{4}{x})}^{x}$
2895	Evaluate the Limit	limit as x approaches 8 of (5x^2+7x-9)/(-6x^2+2)	$lim_{x \to 8} \frac{5 x^{2} + 7 x - 9}{- 6 x^{2} + 2}$
2896	Evaluate the Limit	limit as x approaches 6 of (x^3-36x)/(x-6)	$lim_{x \to 6} \frac{x^{3} - 36 x}{x - 6}$
2897	Evaluate the Limit	limit as x approaches 5 of x	$lim_{x \to 5} x$
2898	Evaluate the Limit	limit as x approaches 4 of (x-4)/(x^3-64)	$lim_{x \to 4} \frac{x - 4}{x^{3} - 64}$
2899	Evaluate the Limit	limit as x approaches 5 of 1/(x-5)	$lim_{x \to 5} \frac{1}{x - 5}$
2900	Evaluate the Limit	limit as x approaches -1 of (2x^2+3x+1)/(x^2-2x-3)	$lim_{x \to - 1} \frac{2 x^{2} + 3 x + 1}{x^{2} - 2 x - 3}$