Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
83401	Find the Antiderivative	f(x)=1/3x^3	$f (x) = \frac{1}{3} x^{3}$
83402	Evaluate the Integral	integral from 2 to 4 of 1 with respect to x integral from x to 2x of y/(3x) with respect to y	$\int_{2}^{4} d x \int_{x}^{2 x} \frac{y}{3 x} d y$
83403	Find the Derivative - d/dx	- square root of x^2+1	$- \sqrt{x^{2} + 1}$
83404	Evaluate the Integral	integral of [2/x+3e^x] with respect to x	$\int [\frac{2}{x} + 3 e^{x}] d x$
83405	Find the Antiderivative	f'(x)=x	$f' (x) = x$
83406	Evaluate the Integral	integral of (2-3/(x^10)) with respect to x	$\int (2 - \frac{3}{x^{10}}) d x$
83407	Evaluate the Integral	integral of (9x)/((x^2+1)^4) with respect to x	$\int \frac{9 x}{{(x^{2} + 1)}^{4}} d x$
83408	Evaluate the Integral	integral from 0 to natural log of 7 of (e^x)/(e^x+2) with respect to x	$\int_{0}^{\ln (7)} \frac{e^{x}}{e^{x} + 2} d x$
83409	Find dQ/dK	Q=5L+6LK^2+8K	$Q = 5 L + 6 L K^{2} + 8 K$
83410	Find the Antiderivative	3^(1-2x)	$3^{1 - 2 x}$
83411	Find the Antiderivative	x*e^(x/3)	$x \cdot e^{\frac{x}{3}}$
83412	Find the Area Between the Curves	y=x^3-15x , y=x	$y = x^{3} - 15 x$ , $y = x$
83413	Find the Second Derivative	f(x)=1/4x^-3-2/3-2/3x^6+1/2x^4	$f (x) = \frac{1}{4} x^{- 3} - \frac{2}{3} - \frac{2}{3} x^{6} + \frac{1}{2} x^{4}$
83414	Find the Derivative - d/dx	1/(1-e^(-x))	$\frac{1}{1 - e^{- x}}$
83415	Find the Derivative Using Chain Rule - d/dx	y=arctan(4x^2-3)	$y = \arctan (4 x^{2} - 3)$
83416	Find the Center and Radius	x^2-12x+84=-y^2+16y	$x^{2} - 12 x + 84 = - y^{2} + 16 y$
83417	Evaluate the Integral	integral of e^(x^2+4x+3)(x+2) with respect to x	$\int e^{x^{2} + 4 x + 3} (x + 2) d x$
83418	Evaluate the Integral	integral of 1/((x^2-1)^2) with respect to x	$\int \frac{1}{{(x^{2} - 1)}^{2}} d x$
83419	Find the Derivative - d/dx	y=3e^pi-pi^3	$y = 3 e^{π} - π^{3}$
83420	Find the Average Value of the Function	f(x)=x*e^x , [0,1]	$f (x) = x \cdot e^{x}$ , $[0, 1]$
83421	Eliminate the Parameter	x(t)=t^2-4t and y(t)=2t^3-6t	$x (t) = t^{2} - 4 t$ and $y (t) = 2 t^{3} - 6 t$
83422	Evaluate the Integral	integral of 1/(3+4x^2)(8x) with respect to x	$\int \frac{1}{3 + 4 x^{2}} (8 x) d x$
83423	Find dz/dx	z=x^y	$z = x^{y}$
83424	Evaluate the Limit	limit as x approaches 1 of (2+4x)/3=2	$lim_{x \to 1} \frac{2 + 4 x}{3} = 2$
83425	Evaluate the Integral	integral of (6x square root of 2x^2-7)/5 with respect to x	$\int \frac{6 x \sqrt{2 x^{2} - 7}}{5} d x$
83426	Find the Inflection Points	3/20x^5-2x^4	$\frac{3}{20} x^{5} - 2 x^{4}$
83427	Find the Derivative - d/dx	y = square root of 100	$y = \sqrt{100}$
83428	Evaluate the Integral	integral from 2 to 4 of (1/2x^3-3x+2) with respect to x	$\int_{2}^{4} (\frac{1}{2} x^{3} - 3 x + 2) d x$
83429	Evaluate the Integral	integral from 0 to 4 of 24-(6x^3)/12 with respect to x	$\int_{0}^{4} 24 - \frac{6 x^{3}}{12} d x$
83430	Find the Derivative - d/dt	2e^(3t)-e^(2t)	$2 e^{3 t} - e^{2 t}$
83431	Find the Tangent Line at (1/2,8)	f(t)=t^-3 ;, (1/2,8)	$f (t) = t^{- 3}$ ;, $(\frac{1}{2}, 8)$
83432	Find dx/dy	y=1/(sin(20x))	$y = \frac{1}{\sin (20 x)}$
83433	Evaluate the Integral	integral of ((3w^2)/2-2/(3w^2)) with respect to w	$\int (\frac{3 w^{2}}{2} - \frac{2}{3 w^{2}}) d w$
83434	Find the Derivative - d/dx	((5x)/(6-5x^3))^3	${(\frac{5 x}{6 - 5 x^{3}})}^{3}$
83435	Find the Derivative - d/dt	e^(-(t-3)^2)	$e^{- {(t - 3)}^{2}}$
83436	Find Where Increasing/Decreasing	f(x)=- square root of x^3+8	$f (x) = - \sqrt{x^{3} + 8}$
83437	Find the Antiderivative	f(x)=cos(pi/6-5x)	$f (x) = \cos (\frac{π}{6} - 5 x)$
83438	Find Where Increasing/Decreasing	f(x)=-1/3\|x-2\|+4	$f (x) = - \frac{1}{3} \| x - 2 \| + 4$
83439	Find the Antiderivative	e^x+2	$e^{x} + 2$
83440	Evaluate Using L'Hospital's Rule	limit as x approaches -1 of (3x-9x^2)/(2 natural log of -1-2x-2)	$lim_{x \to - 1} \frac{3 x - 9 x^{2}}{2 \ln (- 1 - 2 x) - 2}$
83441	Find the Maximum/Minimum Value	y=e^x	$y = e^{x}$
83442	Find Where Increasing/Decreasing	y=x^2e^(-x)	$y = x^{2} e^{- x}$
83443	Evaluate the Limit	limit as x approaches pi/3 of (2cos(x)^2+3cos(x)-2)/(2cos(x)-1)	$lim_{x \to \frac{π}{3}} \frac{2 \cos^{2} (x) + 3 \cos (x) - 2}{2 \cos (x) - 1}$
83444	Evaluate the Integral	integral of ( cube root of x)/3 with respect to x	$\int \frac{\sqrt[3]{x}}{3} d x$
83445	Find the Antiderivative	sin(2x)*e^(sin(x)^2)	$\sin (2 x) \cdot e^{\sin^{2} (x)}$
83446	Evaluate the Limit	limit as x approaches 0 of ((x+1)^2-1)/(x^2+x)	$lim_{x \to 0} \frac{{(x + 1)}^{2} - 1}{x^{2} + x}$
83447	Find the Derivative - d/dt	2/(2t)	$\frac{2}{2 t}$
83448	Find the Antiderivative	4x* natural log of x	$4 x \cdot \ln (x)$
83449	Find the Integral	x square root of x^2+1	$x \sqrt{x^{2} + 1}$
83450	Find the Maximum/Minimum Value	f(x)=x^4+4x^3-8x^2+1	$f (x) = x^{4} + 4 x^{3} - 8 x^{2} + 1$
83451	Evaluate the Integral	integral of 1/(a^2+x^2) with respect to a	$\int \frac{1}{a^{2} + x^{2}} d a$
83452	Find Where Increasing/Decreasing	y=(2/3)^x+2	$y = {(\frac{2}{3})}^{x} + 2$
83453	Find the Derivative - d/dx	(3+2x^2)/(1-5x^2)	$\frac{3 + 2 x^{2}}{1 - 5 x^{2}}$
83454	Find dy/dx	square root of x+y=5y^2	$\sqrt{x + y} = 5 y^{2}$
83455	Evaluate the Integral	integral of (x^3+5x^2-2)e^(2x) with respect to x	$\int (x^{3} + 5 x^{2} - 2) e^{2 x} d x$
83456	Evaluate the Integral	integral of (8/2x^8-x^6+7x^-4+1/2x^2+10) with respect to x	$\int (\frac{8}{2} x^{8} - x^{6} + 7 x^{- 4} + \frac{1}{2} x^{2} + 10) d x$
83457	Find the Derivative - d/dθ	x = square root of (1+cos(theta))/(1-cos(theta))	$x = \sqrt{\frac{1 + \cos (θ)}{1 - \cos (θ)}}$
83458	Find the Antiderivative	(dx)/(x^2-2x+10)	$\frac{d x}{x^{2} - 2 x + 10}$
83459	Find the Derivative - d/dx	y=( natural log of 1-x^2)/(x-1)	$y = \frac{\ln (1 - x^{2})}{x - 1}$
83460	Find dy/dx	2y=-2x^2+y^2	$2 y = - 2 x^{2} + y^{2}$
83461	Evaluate the Integral	integral from 0 to pi/8 of cos(2x)^4 with respect to x	$\int_{0}^{\frac{π}{8}} \cos^{4} (2 x) d x$
83462	Find the Maximum/Minimum Value	(x+2)(x+1)(x-3)	$(x + 2) (x + 1) (x - 3)$
83463	Evaluate the Integral	integral of 3/( fourth root of 2x+5) with respect to x	$\int \frac{3}{\sqrt[4]{2 x + 5}} d x$
83464	Find the Integral	e^(-st)	$e^{- s t}$
83465	Evaluate the Integral	integral of (5x^-3-3x^5+4x^4) with respect to x	$\int (5 x^{- 3} - 3 x^{5} + 4 x^{4}) d x$
83466	Evaluate the Integral	integral of ex with respect to x	$\int e x d x$
83467	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (cos(x)-1)/x	$lim_{x \to 0} \frac{\cos (x) - 1}{x}$
83468	Find the Maximum/Minimum Value	f(x)=3x^4-4x^3-12x^2	$f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2}$
83469	Find the Derivative - d/dx	-x^3(3x^4-2)	$- x^{3} (3 x^{4} - 2)$
83470	Find the Derivative - d/dt	y=3t^7-6t^4+8t^3-12^t+18	$y = 3 t^{7} - 6 t^{4} + 8 t^{3} - 12^{t} + 18$
83471	Evaluate the Integral	integral from 0 to pi/2 of cos(x)^7sin(x)^5 with respect to x	$\int_{0}^{\frac{π}{2}} \cos^{7} (x) \sin^{5} (x) d x$
83472	Integrate Using u-Substitution	integral of tan(x)^2 with respect to x	$\int \tan^{2} (x) d x$
83473	Evaluate the Limit	limit as t approaches 1 of ((t^2-1)/(t^2-3t-4))^1	$lim_{t \to 1} {(\frac{t^{2} - 1}{t^{2} - 3 t - 4})}^{1}$
83474	Find the Antiderivative	3/(2x-5)-4	$\frac{3}{2 x - 5} - 4$
83475	Find the Antiderivative	4-3(1+x^2)^-1	$4 - 3 {(1 + x^{2})}^{- 1}$
83476	Find the Derivative - d/dx	ke^(-2x)-2x^(k^2)	$k e^{- 2 x} - 2 x^{k^{2}}$
83477	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (3e^(x-1)-3)/(3cos(x-1)-3x^3)	$lim_{x \to 1} \frac{3 e^{x - 1} - 3}{3 \cos (x - 1) - 3 x^{3}}$
83478	Evaluate the Limit	limit as x approaches 0 of (-e^(2x))/((2-e^(2x))^2)	$lim_{x \to 0} \frac{- e^{2 x}}{{(2 - e^{2 x})}^{2}}$ ?
83479	Find dx/dy	y^3-xy^2+x^3=5	$y^{3} - x y^{2} + x^{3} = 5$
83480	Determine if Continuous	f(x)=x^2+ square root of 7-x	$f (x) = x^{2} + \sqrt{7 - x}$
83481	Find the Derivative - d/dx	4x^-2+1/4x^2+4	$4 x^{- 2} + \frac{1}{4} x^{2} + 4$
83482	Find dy/dx	square root of x+4y^2=y	$\sqrt{x + 4 y^{2}} = y$
83483	Find dy/dx	y=(2-3x)/(3+x^2)	$y = \frac{2 - 3 x}{3 + x^{2}}$
83484	Integrate Using u-Substitution	integral of sin(5x) with respect to x	$\int \sin (5 x) d x$
83485	Find the Derivative - d/dx	e^(x^2)-1	$e^{x^{2}} - 1$
83486	Integrate Using u-Substitution	integral of square root of 4-x^2 with respect to x	$\int \sqrt{4 - x^{2}} d x$
83487	Find dy/dx	y=(9x^2-2x+2)^(-3/4)	$y = {(9 x^{2} - 2 x + 2)}^{- \frac{3}{4}}$
83488	Evaluate the Integral	integral of (-4/(x^3)-8/(x^5)) with respect to x	$\int (- \frac{4}{x^{3}} - \frac{8}{x^{5}}) d x$
83489	Evaluate the Limit	limit as z approaches 2 of (z-2)/( square root of 3-z-1)	$lim_{z \to 2} \frac{z - 2}{\sqrt{3 - z} - 1}$
83490	Find the Integral	(7x^4+5)/(x^2+1)	$\frac{7 x^{4} + 5}{x^{2} + 1}$
83491	Find the Derivative - d/dx	y=(2-7x)^2	$y = {(2 - 7 x)}^{2}$
83492	Find the Derivative - d/dx	3x+x^2	$3 x + x^{2}$
83493	Find dy/dx	y=3^(2x)	$y = 3^{2 x}$
83494	Evaluate the Integral	2 integral from 0 to 1 of x^2 with respect to x	$2 \int_{0}^{1} x^{2} d x$
83495	Find the Derivative - d/dx	arctan(x^2+1)	$\arctan (x^{2} + 1)$
83496	Evaluate the Limit	limit as x approaches 0 of (3x+4x^2-x^3)^4	$lim_{x \to 0} {(3 x + 4 x^{2} - x^{3})}^{4}$
83497	Evaluate the Integral	integral from -5 to 5 of square root of 5^2-x^2 with respect to x	$\int_{- 5}^{5} \sqrt{5^{2} - x^{2}} d x$
83498	Evaluate the Limit	limit as x approaches 1 of (xe^x-e)/(x^2-1)	$lim_{x \to 1} \frac{x e^{x} - e}{x^{2} - 1}$
83499	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of cos(x)^(1/x)	$lim_{x \to 0^{+}} {\cos (x)}^{\frac{1}{x}}$
83500	Evaluate the Integral	integral of x*e^(-x^2) with respect to x	$\int x \cdot e^{- x^{2}} d x$