Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
80601	Evaluate the Integral	integral from 0 to 1 of square root of x(x+1) with respect to x	$\int_{0}^{1} \sqrt{x} (x + 1) d x$
80602	Find dy/dx	y = square root of x+x^(3/2)-8x	$y = \sqrt{x} + x^{\frac{3}{2}} - 8 x$
80603	Find the Antiderivative	- square root of x	$- \sqrt{x}$
80604	Find the Derivative - d/dx	y=-tan(10x^2)	$y = - \tan (10 x^{2})$
80605	Find the Derivative Using Product Rule - d/dx	y=x^2(x-1)	$y = x^{2} (x - 1)$
80606	Find dy/dx	3x^2y^3-x+y=25	$3 x^{2} y^{3} - x + y = 25$
80607	Find the Third Derivative	18x^3-12x	$18 x^{3} - 12 x$
80608	Evaluate the Limit	limit as x approaches -1/6 of (x+6x^2)/(x^2-1/36)	$lim_{x \to - \frac{1}{6}} \frac{x + 6 x^{2}}{x^{2} - \frac{1}{36}}$
80609	Evaluate Using L'Hospital's Rule	limit as x approaches pi/2 of (3cos(x))/(2x-pi)	$lim_{x \to \frac{π}{2}} \frac{3 \cos (x)}{2 x - π}$
80610	Find the Antiderivative	(e^x)/(2^x)	$\frac{e^{x}}{2^{x}}$
80611	Evaluate the Integral	integral of 1/(x^3-2x^2+x) with respect to xdx	$\int \frac{1}{x^{3} - 2 x^{2} + x} d x d x$
80612	Evaluate the Limit	limit as x approaches 2 from the left of x^3-2x^2-3	$lim_{x \to 2^{-}} x^{3} - 2 x^{2} - 3$
80613	Find the Percentage Rate of Change	m(t)=(4/5)^t	$m (t) = {(\frac{4}{5})}^{t}$
80614	Find dx/dy	y = square root of x+x^(3/2)-8x	$y = \sqrt{x} + x^{\frac{3}{2}} - 8 x$
80615	Integrate Using Partial Fractions	integral of (3x^3-3x+4)/(4x^2-4) with respect to x	$\int \frac{3 x^{3} - 3 x + 4}{4 x^{2} - 4} d x$
80616	Find the Derivative of the Integral	integral from -2 to 2 of (x^3cos(x/2)+1/2) square root of 4-x^2dx with respect to x	$\int_{- 2}^{2} (x^{3} \cos (\frac{x}{2}) + \frac{1}{2}) \sqrt{4 - x^{2} d x} d x$
80617	Find the Antiderivative	x* natural log of x	$x \cdot \ln (x)$
80618	Evaluate the Integral	integral from 5 to square root of x of f(t) with respect to t=x^2	$\int_{5}^{\sqrt{x}} f (t) d t = x^{2}$
80619	Find Where Increasing/Decreasing	f(x)=-3/5x^5+9x^4-32x^3+49	$f (x) = - \frac{3}{5} x^{5} + 9 x^{4} - 32 x^{3} + 49$
80620	Evaluate the Integral	integral from 0 to 1 of (x^2-1)e^x with respect to x	$\int_{0}^{1} (x^{2} - 1) e^{x} d x$
80621	Evaluate the Integral	integral of (2x+2)/( square root of 3x^2+6x) with respect to x	$\int \frac{2 x + 2}{\sqrt{3 x^{2} + 6 x}} d x$
80622	Evaluate the Limit	limit as x approaches -2 of (-6\|x\|+12)/(3x+6)	$lim_{x \to - 2} \frac{- 6 \| x \| + 12}{3 x + 6}$
80623	Find the Antiderivative	(x^3)/2-3x^-2-2x^3-x^(3/2)	$\frac{x^{3}}{2} - 3 x^{- 2} - 2 x^{3} - x^{\frac{3}{2}}$
80624	Find the Antiderivative	sin(x)^3*cos(x)	$\sin^{3} (x) \cdot \cos (x)$
80625	Evaluate the Limit	limit as x approaches 0 from the right of cos(x)^(1/x)	$lim_{x \to 0^{+}} {\cos (x)}^{\frac{1}{x}}$
80626	Evaluate the Limit	limit as x approaches infinity of (-x^2-x)/(-3x^2)	$lim_{x \to \infty} \frac{- x^{2} - x}{- 3 x^{2}}$
80627	Find the Antiderivative	x+1/x	$x + \frac{1}{x}$
80628	Evaluate the Limit	limit as x approaches 4 of 3x- square root of x	$lim_{x \to 4} 3 x - \sqrt{x}$
80629	Evaluate the Integral	integral of (sin(x)^3)(cos(x)) with respect to x	$\int (\sin^{3} (x)) (\cos (x)) d x$
80630	Find the Antiderivative	2/(x^3)-4/(x^2)	$\frac{2}{x^{3}} - \frac{4}{x^{2}}$
80631	Find the Maximum/Minimum Value	h(x)=x^5+x^4	$h (x) = x^{5} + x^{4}$
80632	Evaluate the Limit	limit as x approaches 1 of (x^2-x-2)/(x^2-2x)	$lim_{x \to 1} \frac{x^{2} - x - 2}{x^{2} - 2 x}$
80633	Evaluate the Limit	limit as x approaches infinity of (5+x-4x^2)/( square root of 1+x^2+2x^4)	$lim_{x \to \infty} \frac{5 + x - 4 x^{2}}{\sqrt{1 + x^{2} + 2 x^{4}}}$
80634	Find the Antiderivative	1/(x^2+x-2)	$\frac{1}{x^{2} + x - 2}$
80635	Integrate Using u-Substitution	integral of (5-e^x)/(e^(2x)) with respect to x	$\int \frac{5 - e^{x}}{e^{2 x}} d x$
80636	Find the Antiderivative	2/(x^3)-3/x	$\frac{2}{x^{3}} - \frac{3}{x}$
80637	Find the Derivative - d/dx	(sin(-x))	$(\sin (- x))$
80638	Find the Derivative - d/dt	2+5arctan(t/2)	$2 + 5 \arctan (\frac{t}{2})$
80639	Find the Antiderivative	2/(4x-3)	$\frac{2}{4 x - 3}$
80640	Evaluate the Integral	integral from 0 to pi of integral from 0 to 2pi of 0 with respect to theta with respect to x	$\int_{0}^{π} \int_{0}^{2 π} 0 d θ d x$
80641	Evaluate the Limit	limit as x approaches 0 of ( square root of 1+x-1)/( square root of 4+x-2)	$lim_{x \to 0} \frac{\sqrt{1 + x} - 1}{\sqrt{4 + x} - 2}$
80642	Evaluate the Integral	integral of 2/( square root of x^3) with respect to x	$\int \frac{2}{\sqrt{x^{3}}} d x$
80643	Find Where Increasing/Decreasing	f(x)=2^(x+3)-5	$f (x) = 2^{x + 3} - 5$
80644	Find the Derivative - d/dx	-15/(16(x+1)^(7/2))	$\frac{- 15}{16 {(x + 1)}^{\frac{7}{2}}}$
80645	Find the Antiderivative	x square root of 4-x^2	$x \sqrt{4 - x^{2}}$
80646	Find the Derivative - d/dx	e^(-x)(x^2+2x)	$e^{- x} (x^{2} + 2 x)$
80647	Find Where Increasing/Decreasing	x^4+8x^3+16x^2	$x^{4} + 8 x^{3} + 16 x^{2}$
80648	Evaluate the Integral	integral from 0 to 1 of (e^(-x)+e^x)/(e^x) with respect to x	$\int_{0}^{1} \frac{e^{- x} + e^{x}}{e^{x}} d x$
80649	Evaluate the Integral	integral from 0 to 1 of (e^(-x)+e^x)/(e^(-x)) with respect to x	$\int_{0}^{1} \frac{e^{- x} + e^{x}}{e^{- x}} d x$
80650	Find the Antiderivative	(2x-1)/((x+1)^2)	$\frac{2 x - 1}{{(x + 1)}^{2}}$
80651	Evaluate the Integral	integral of 1/( square root of 8+2x-x^2) with respect to x	$\int \frac{1}{\sqrt{8 + 2 x - x^{2}}} d x$
80652	Find the Antiderivative	(sin(x))/(1+3cos(x))	$\frac{\sin (x)}{1 + 3 \cos (x)}$
80653	Evaluate the Integral	integral from 0 to 1 of (e^(-x)+1)/(e^(-x)) with respect to x	$\int_{0}^{1} \frac{e^{- x} + 1}{e^{- x}} d x$
80654	Find Where Increasing/Decreasing	y=(7/2)^x	$y = {(\frac{7}{2})}^{x}$
80655	Evaluate the Integral	integral from 0 to 2 of (2x^3-6x+3/(x^2+1)) with respect to x	$\int_{0}^{2} (2 x^{3} - 6 x + \frac{3}{x^{2} + 1}) d x$
80656	Find Where Increasing/Decreasing	f(x)=3/4x^4+x^3-135x^2+19	$f (x) = \frac{3}{4} x^{4} + x^{3} - 135 x^{2} + 19$
80657	Find the Inflection Points	f(x)=1/10x^5-2x^4+12x^3	$f (x) = \frac{1}{10} x^{5} - 2 x^{4} + 12 x^{3}$
80658	Find the Antiderivative	(sin(x))/x	$\frac{\sin (x)}{x}$
80659	Find the Absolute Max and Min over the Interval	f(x)=3x^2-x^3 , [1,5/2]	$f (x) = 3 x^{2} - x^{3}$ , $[1, \frac{5}{2}]$
80660	Evaluate the Limit	limit as x approaches infinity of (7+x^-3)/(3x^-3+5)	$lim_{x \to \infty} \frac{7 + x^{- 3}}{3 x^{- 3} + 5}$
80661	Find the Absolute Max and Min over the Interval	f(x)=(x^2)/((x-1)^2) on interval -2 , -1	$f (x) = \frac{x^{2}}{{(x - 1)}^{2}}$ on interval $- 2$ , $- 1$
80662	Evaluate the Limit	limit as x approaches 0 of (e^x-1-2x)/(x^2)	$lim_{x \to 0} \frac{e^{x} - 1 - 2 x}{x^{2}}$
80663	Find the Derivative of the Integral	G(x) = integral from 1 to x of sin(t^2) with respect to t	$G (x) = \int_{1}^{x} \sin (t^{2}) d t$
80664	Find dy/dx	y=x+y^2	$y = x + y^{2}$
80665	Find the Slope of the Tangent Line at (25,5)	y = square root of x , (25,5)	$y = \sqrt{x}$ , $(25, 5)$
80666	Find the Concavity	f(x)=1/10x^5-12x^3	$f (x) = \frac{1}{10} x^{5} - 12 x^{3}$
80667	Find the Center and Radius	(x-h)^2(y-k)^2=r^2	${(x - h)}^{2} {(y - k)}^{2} = r^{2}$
80668	Find the Antiderivative	(x^2)/(x-1)	$\frac{x^{2}}{x - 1}$
80669	Find the Derivative - d/dx	square root of 2x^3+x+1	$\sqrt{2 x^{3} + x + 1}$
80670	Find the Derivative - d/dx	e^(2x-6)-e	$e^{2 x - 6} - e$
80671	Find the Antiderivative	f(x)=4+x	$f (x) = 4 + x$
80672	Find the Percentage Rate of Change	f(t)=80(3/5)^t	$f (t) = 80 {(\frac{3}{5})}^{t}$
80673	Find the Antiderivative	x/(sin(x)^2)	$\frac{x}{\sin^{2} (x)}$
80674	Find the Antiderivative	f(x)=3/((5-7x)^4)	$f (x) = \frac{3}{{(5 - 7 x)}^{4}}$
80675	Find the Antiderivative	tan(x)^4	$\tan^{4} (x)$
80676	Find the Antiderivative	9xcos(3x)	$9 x \cos (3 x)$
80677	Find the Derivative - d/dx	(1/x)^x	${(\frac{1}{x})}^{x}$
80678	Evaluate the Limit	limit as x approaches 0 of (5x-3sin(x))/(7x+tan(x))	$lim_{x \to 0} \frac{5 x - 3 \sin (x)}{7 x + \tan (x)}$
80679	Evaluate the Limit	limit as x approaches 1 from the right of square root of 4x-4	$lim_{x \to 1^{+}} \sqrt{4 x - 4}$
80680	Find Where Increasing/Decreasing	f(x)=1/2*e^(-x)-1	$f (x) = \frac{1}{2} \cdot e^{- x} - 1$
80681	Find the Antiderivative	(e^x)/(1+e^x)	$\frac{e^{x}}{1 + e^{x}}$
80682	Find the Derivative - d/dx	y = square root of 2^x+2e^x	$y = \sqrt{2^{x} + 2 e^{x}}$
80683	Evaluate the Limit	limit as x approaches 2 of \|f(x)\|	$lim_{x \to 2} \| f (x) \|$
80684	Find the Concavity	f(x)=-2/5x^6+5x^4	$f (x) = - \frac{2}{5} x^{6} + 5 x^{4}$
80685	Find the Maximum/Minimum Value	f(x)=x^4+x^3-4x^2+5	$f (x) = x^{4} + x^{3} - 4 x^{2} + 5$
80686	Find the Antiderivative	2x(1+3x^3)	$2 x (1 + 3 x^{3})$
80687	Evaluate the Integral	integral of ((8-4x+6x^(4/3)+12 cube root of x^8)/(4 cube root of x)) with respect to x	$\int (\frac{8 - 4 x + 6 x^{\frac{4}{3}} + 12 \sqrt[3]{x^{8}}}{4 \sqrt[3]{x}}) d x$
80688	Find dy/dx	e^y+xy=e	$e^{y} + x y = e$
80689	Find the Maximum/Minimum Value	f(x) = square root of 2x-5	$f (x) = \sqrt{2 x - 5}$
80690	Evaluate the Limit	limit as x approaches c of ((f(x))/(2g(x)))+h(x)	$lim_{x \to c} (\frac{f (x)}{2 g (x)}) + h (x)$
80691	Evaluate the Limit	limit as x approaches 0 of (sin(2x)+5tan(3x))/x	$lim_{x \to 0} \frac{\sin (2 x) + 5 \tan (3 x)}{x}$
80692	Find the Antiderivative	(x^3)/(x-1)	$\frac{x^{3}}{x - 1}$
80693	Find the Derivative of the Integral	G(x) = integral from 4 to x of square root of 1+t^2 with respect to t	$G (x) = \int_{4}^{x} \sqrt{1 + t^{2}} d t$
80694	Evaluate the Integral	integral of (4x^3)/(2x+3) with respect to x	$\int \frac{4 x^{3}}{2 x + 3} d x$
80695	Find the Derivative - d/dx	3/(8(x+1)^(5/2))	$\frac{3}{8 {(x + 1)}^{\frac{5}{2}}}$
80696	Evaluate the Summation	7 sum from m=1 to 5 of -7+2m	$7 \sum_{m = 1}^{5} - 7 + 2 m$
80697	Evaluate the Limit	limit as x approaches 2 of (-4f(x))/(g(x))+e^(x-2)-1	$lim_{x \to 2} \frac{- 4 f (x)}{g (x)} + e^{x - 2} - 1$
80698	Evaluate the Integral	integral from 0 to 2 of x/(1-x) with respect to x	$\int_{0}^{2} \frac{x}{1 - x} d x$
80699	Evaluate the Integral	integral of x(x^3+2/(x^3)) with respect to x	$\int x (x^{3} + \frac{2}{x^{3}}) d x$
80700	Evaluate the Limit	limit as x approaches 1/2 of (xcos(pix))/(e^x- square root of e)	$lim_{x \to \frac{1}{2}} \frac{x \cos (π x)}{e^{x} - \sqrt{e}}$