Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
85101	Find the Antiderivative	f(x)=e^(2x+3)	$f (x) = e^{2 x + 3}$
85102	Evaluate the Limit	limit as x approaches -pi/2 of cos(5x-cos(5x))	$lim_{x \to - \frac{π}{2}} \cos (5 x - \cos (5 x))$
85103	Find the Integral	( natural log of x)/xdx	$\frac{\ln (x)}{x} d x$
85104	Find the Derivative - d/dx	natural log of cos(x)^2	$\ln (\cos^{2} (x))$
85105	Find the Antiderivative	f(x)=5x^-3+2x-y	$f (x) = 5 x^{- 3} + 2 x - y$
85106	Find dy/dx	sin(x^3y)=x^3	$\sin (x^{3} y) = x^{3}$
85107	Find the Derivative - d/dx	sin(4x^2+3x)	$\sin (4 x^{2} + 3 x)$
85108	Find the Derivative - d/dv	1/v	$\frac{1}{v}$
85109	Evaluate the Integral	integral from 0 to 9 of pi( square root of x)^2 with respect to x	$\int_{0}^{9} π {(\sqrt{x})}^{2} d x$
85110	Integrate By Parts	integral of x*e^x with respect to x	$\int x \cdot e^{x} d x$
85111	Find dy/dx	y^4=3xy-5	$y^{4} = 3 x y - 5$
85112	Find the Center and Radius	x^2+y^2	$x^{2} + y^{2}$
85113	Evaluate the Integral	integral from 2 to 3 of 1/(x^2-4x) with respect to x	$\int_{2}^{3} \frac{1}{x^{2} - 4 x} d x$
85114	Evaluate the Summation	7 sum from t=4 to 9 of t^2-7t	$7 \sum_{t = 4}^{9} t^{2} - 7 t$
85115	Find the Antiderivative	x log of x	$x \log (x)$
85116	Find the Derivative - d/dx	( square root of 1+2x-1)/x	$\frac{\sqrt{1 + 2 x} - 1}{x}$
85117	Find the Antiderivative	5/x+ square root of x^3	$\frac{5}{x} + \sqrt{x^{3}}$
85118	Evaluate the Limit	limit as x approaches -1 of (1- square root of x^2+2x+2)/(1+x)	$lim_{x \to - 1} \frac{1 - \sqrt{x^{2} + 2 x + 2}}{1 + x}$
85119	Evaluate the Limit	limit as n approaches infinity of (4n^2)/(n^2+10000n)	$lim_{n \to \infty} \frac{4 n^{2}}{n^{2} + 10000 n}$
85120	Find the Maximum/Minimum Value	y=1/3x^3+x^2-3x-8	$y = \frac{1}{3} x^{3} + x^{2} - 3 x - 8$
85121	Find dy/dx	y=(2x^2-1)/(5x+2)	$y = \frac{2 x^{2} - 1}{5 x + 2}$
85122	Find the Third Derivative	y=x square root of x-1	$y = x \sqrt{x - 1}$
85123	Integrate Using u-Substitution	integral of x^2(2x^3-1)^4 with respect to x	$\int x^{2} {(2 x^{3} - 1)}^{4} d x$
85124	Find dy/dx	-y^3-4x^2=-4x^3	$- y^{3} - 4 x^{2} = - 4 x^{3}$
85125	Find dx/dy	2y^3+4x^2-y=x^6	$2 y^{3} + 4 x^{2} - y = x^{6}$
85126	Evaluate the Limit	limit as x approaches 0 of (-1-1)/(-1+1)	$lim_{x \to 0} \frac{- 1 - 1}{- 1 + 1}$
85127	Evaluate the Integral	integral of (e^( square root of x))/(2 square root of x) with respect to x	$\int \frac{e^{\sqrt{x}}}{2 \sqrt{x}} d x$
85128	Find the Maximum/Minimum Value	y=1/2(x-6)^2	$y = \frac{1}{2} {(x - 6)}^{2}$
85129	Find the Second Derivative	f(x)=cos(x^2)	$f (x) = \cos (x^{2})$
85130	Evaluate the Limit	limit as x approaches 8 from the right of ( square root of x-8)/x	$lim_{x \to 8^{+}} \frac{\sqrt{x - 8}}{x}$
85131	Integrate By Parts	integral from 1 to e of x natural log of x with respect to x	$\int_{1}^{e} x \ln (x) d x$
85132	Evaluate the Limit	limit as x approaches infinity of (1+x)^(3/x)	$lim_{x \to \infty} {(1 + x)}^{\frac{3}{x}}$
85133	Find the Derivative - d/dx	natural log of e^(3x)+x	$\ln (e^{3 x} + x)$
85134	Find the Derivative - d/dt	y=2e^(cos(t))	$y = 2 e^{\cos (t)}$
85135	Find the Maximum/Minimum Value	Let g(x)=x^4-x^5	Let $g (x) = x^{4} - x^{5}$
85136	Find the Domain and Range	f(x)=2x if x<=0; 2 if x>0	$f (x) = {\begin{cases} 2 x & x \leq 0 \\ 2 & x > 0 \end{cases}$
85137	Find the Tangent Line at (-2,-3)	f(x)=x^3+x+7 ;, (-2,-3)	$f (x) = x^{3} + x + 7$ ;, $(- 2, - 3)$
85138	Find Where Increasing/Decreasing	g'(x)=x/(x+3)	$g' (x) = \frac{x}{x + 3}$
85139	Evaluate the Integral	integral of (2x-5)/(x^2-5x-1) with respect to x	$\int \frac{2 x - 5}{x^{2} - 5 x - 1} d x$
85140	Find dy/dx	cos(5x+y)=y	$\cos (5 x + y) = y$
85141	Find the Integral	natural log of 1+x	$\ln (1 + x)$
85142	Evaluate the Integral	integral from 0 to 2 of pi(4-2x)^2 with respect to x	$\int_{0}^{2} π {(4 - 2 x)}^{2} d x$
85143	Integrate Using Partial Fractions	integral of (2x^2+3)/(x^3-2x^2+x) with respect to x	$\int \frac{2 x^{2} + 3}{x^{3} - 2 x^{2} + x} d x$
85144	Find the Derivative - d/dx	y=(-x^3*cos(x^3))/3	$y = \frac{- x^{3} \cdot \cos (x^{3})}{3}$
85145	Find the Derivative - d/dx	(e^(2x))	$(e^{2 x})$
85146	Find the Derivative - d/dx	(sin(-8x))	$(\sin (- 8 x))$
85147	Evaluate the Integral	integral of 6/(5 cube root of x) with respect to x	$\int \frac{6}{5 \sqrt[3]{x}} d x$
85148	Evaluate the Limit	limit as x approaches 8 of (2/x-1/(x-4))/(x-8)	$lim_{x \to 8} \frac{\frac{2}{x} - \frac{1}{x - 4}}{x - 8}$
85149	Find the Antiderivative	(e^x+1)^2	${(e^{x} + 1)}^{2}$
85150	Find the Maximum/Minimum Value	f(x)=x^5-4x^3+4x-1	$f (x) = x^{5} - 4 x^{3} + 4 x - 1$
85151	Find dy/dx	y=arcsin(x/4)	$y = \arcsin (\frac{x}{4})$
85152	Evaluate Using Summation Formulas	sum from i=1 to 9 of -28(-1/2)^(i-1)	$\sum_{i = 1}^{9} - 28 {(- \frac{1}{2})}^{i - 1}$
85153	Evaluate the Limit	limit as x approaches 0 of (x+e^x)^(1/x)	$lim_{x \to 0} {(x + e^{x})}^{\frac{1}{x}}$
85154	Evaluate the Limit	limit as t approaches -2 of t^3(6-4t^2)	$lim_{t \to - 2} t^{3} (6 - 4 t^{2})$
85155	Find the Critical Points	Let f(x)=2x^3-9x^2+12x	Let $f (x) = 2 x^{3} - 9 x^{2} + 12 x$
85156	Evaluate the Integral	integral from 1 to 2 of (9x^2-4x+1) natural log of x with respect to x	$\int_{1}^{2} (9 x^{2} - 4 x + 1) \ln (x) d x$
85157	Find the Slope	-3x+4	$- 3 x + 4$
85158	Integrate Using u-Substitution	integral of e^(-2x) with respect to x	$\int e^{- 2 x} d x$
85159	Evaluate Using L'Hospital's Rule	limit as x approaches 3 of (sin(2x-6))/( natural log of 4-x)	$lim_{x \to 3} \frac{\sin (2 x - 6)}{\ln (4 - x)}$
85160	Integrate By Parts	integral from 0 to 1 of (r^3)/( square root of 16+r^2) with respect to r	$\int_{0}^{1} \frac{r^{3}}{\sqrt{16 + r^{2}}} d r$
85161	Evaluate the Integral	integral from 0 to 1 of x^7e^(-x^8) with respect to x	$\int_{0}^{1} x^{7} e^{- x^{8}} d x$
85162	Integrate By Parts	integral from 0 to 2pi of t^2sin(2t) with respect to t	$\int_{0}^{2 π} t^{2} \sin (2 t) d t$
85163	Evaluate the Limit	limit as x approaches 4 from the left of (\|5x-20\|)/(x^2-5x+4)	$lim_{x \to 4^{-}} \frac{\| 5 x - 20 \|}{x^{2} - 5 x + 4}$
85164	Evaluate the Integral	integral of (x+4)/(2x+6) with respect to x	$\int \frac{x + 4}{2 x + 6} d x$
85165	Evaluate the Integral	integral of (x-2)/(3x+6) with respect to x	$\int \frac{x - 2}{3 x + 6} d x$
85166	Evaluate the Limit	limit as x approaches b of ((x-b)^30-4x+4b)/(x-b)	$lim_{x \to b} \frac{{(x - b)}^{30} - 4 x + 4 b}{x - b}$
85167	Evaluate the Integral	integral of (3x-2)/( square root of x) with respect to x	$\int \frac{3 x - 2}{\sqrt{x}} d x$
85168	Evaluate the Integral	integral of (pi+e^(3x)) with respect to x	$\int (π + e^{3 x}) d x$
85169	Find the Derivative - d/dx	(cos(-8x))	$(\cos (- 8 x))$
85170	Evaluate the Limit	limit as x approaches infinity of 3x^-2e^x	$lim_{x \to \infty} 3 x^{- 2} e^{x}$
85171	Find the Derivative - d/dx	((x+2)^5-32)/x	$\frac{{(x + 2)}^{5} - 32}{x}$
85172	Find dy/dx	4-xy=y-4x^4	$4 - x y = y - 4 x^{4}$
85173	Evaluate the Integral	integral from 0 to a^(1/5) of x^9 square root of a^2-x^10 with respect to x	$\int_{0}^{a^{\frac{1}{5}}} x^{9} \sqrt{a^{2} - x^{10}} d x$
85174	Evaluate Using L'Hospital's Rule	limit as x approaches -3 of (e^(x+3)-x)/(3sin(x+3)+3x)	$lim_{x \to - 3} \frac{e^{x + 3} - x}{3 \sin (x + 3) + 3 x}$
85175	Find the Derivative - d/dx	d/(dx) natural log of 2x	$\frac{d}{d x} \ln (2 x)$
85176	Find the Maximum/Minimum Value	y=-x^4+9x^2-20	$y = - x^{4} + 9 x^{2} - 20$
85177	Find dy/dx	-xy+2x=1	$- x y + 2 x = 1$
85178	Find Where Increasing/Decreasing	f(x)=-2 log base 3 of x+8	$f (x) = - 2 \log_{3} (x + 8)$
85179	Evaluate the Integral	integral of (-2x^3+4+2x^-3) with respect to x	$\int (- 2 x^{3} + 4 + 2 x^{- 3}) d x$
85180	Find the Antiderivative	f(x)=5*2x	$f (x) = 5 \cdot 2 x$
85181	Find the Derivative - d/dt	2tan(t)	$2 \tan (t)$
85182	Find the Slope	f(x)=2(3x-7)	$f (x) = 2 (3 x - 7)$
85183	Find the Concavity	1/3x^3-3x^2-16x	$\frac{1}{3} x^{3} - 3 x^{2} - 16 x$
85184	Evaluate the Limit	limit as x approaches 6 from the left of (x+9)/(x+6)	$lim_{x \to 6^{-}} \frac{x + 9}{x + 6}$
85185	Find the Fourth Derivative	a_n=n*(n+1)!	$a_{n} = n \cdot (n + 1)!$
85186	Evaluate the Integral	integral from 0 to natural log of square root of 3 of (e^x)/(1+e^(2x)) with respect to x	$\int_{0}^{\ln (\sqrt{3})} \frac{e^{x}}{1 + e^{2 x}} d x$
85187	Find the Antiderivative	sin(pi/2-6x)	$\sin (\frac{π}{2} - 6 x)$
85188	Evaluate the Integral	integral of ( square root of x^5)/4 with respect to x	$\int \frac{\sqrt{x^{5}}}{4} d x$
85189	Evaluate the Limit	limit as x approaches -1 of (x^2+7x+6)/(x^2+x)	$lim_{x \to - 1} \frac{x^{2} + 7 x + 6}{x^{2} + x}$
85190	Find the Second Derivative	f(x)=-5/2x^2-3/2x^-3+2x^3	$f (x) = - \frac{5}{2} x^{2} - \frac{3}{2} x^{- 3} + 2 x^{3}$
85191	Integrate By Parts	integral of cos(x)^3 with respect to x	$\int \cos^{3} (x) d x$
85192	Find dy/dx	x^2y-5y=12	$x^{2} y - 5 y = 12$
85193	Determine if Continuous	f(x)=e^x if x<0; x^2 if x>0	$f (x) = {\begin{cases} e^{x} & x < 0 \\ x^{2} & x > 0 \end{cases}$
85194	Evaluate the Limit	limit as x approaches 2 of ( square root of 2x+5- square root of x+7)/(x-2)	$lim_{x \to 2} \frac{\sqrt{2 x + 5} - \sqrt{x + 7}}{x - 2}$
85195	Find dy/dx	y=(3x^3+5)/(3+2x)	$y = \frac{3 x^{3} + 5}{3 + 2 x}$
85196	Find Where Increasing/Decreasing	y=7500(1+0.03)^x	$y = 7500 {(1 + 0.03)}^{x}$
85197	Find the Antiderivative	-2/( square root of x)	$- \frac{2}{\sqrt{x}}$
85198	Evaluate the Integral	integral from 0 to natural log of 2 of xe^(-x) with respect to x	$\int_{0}^{\ln (2)} x e^{- x} d x$
85199	Evaluate the Limit	limit as x approaches 0 of (tan(2x)^2)/(xsin(3x))	$lim_{x \to 0} \frac{\tan^{2} (2 x)}{x \sin (3 x)}$
85200	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^(-x)-1)/(3tan(2x)-2x^3)	$lim_{x \to 0} \frac{e^{- x} - 1}{3 \tan (2 x) - 2 x^{3}}$