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Popular Calculus Problems

derivative of 3e^xcos(x)	derivative\:3e^{x}\cos(x)
integral of (3x^2+x+3)/((x-1)^3(x^2+1))	\int\:\frac{3x^{2}+x+3}{(x-1)^{3}(x^{2}+1)}dx
integral of 1/((y-1)(y+1))	\int\:\frac{1}{(y-1)(y+1)}dy
integral of 1/(x*(ln(x)))	\int\:\frac{1}{x\cdot\:(\ln(x))}dx
limit as x approaches 1 of-x^2+4x-8	\lim\:_{x\to\:1}(-x^{2}+4x-8)
laplacetransform (3t)/t	laplacetransform\:\frac{3t}{t}
derivative of 1/(2sqrt(x)+1/(5x^{4/5)})	\frac{d}{dx}(\frac{1}{2\sqrt{x}}+\frac{1}{5x^{\frac{4}{5}}})
(\partial)/(\partial x)(6xcos(x)sin(y))	\frac{\partial\:}{\partial\:x}(6x\cos(x)\sin(y))
(\partial)/(\partial z)(4ln((3xy)/(7z)))	\frac{\partial\:}{\partial\:z}(4\ln(\frac{3xy}{7z}))
y^{''}+289y=sec(17x),y(0)=3,y^'(0)=3	y^{\prime\:\prime\:}+289y=\sec(17x),y(0)=3,y^{\prime\:}(0)=3
tangent of y=e^{4x}cos(pix),(0,1)	tangent\:y=e^{4x}\cos(πx),(0,1)
derivative of e^{0.5x}	\frac{d}{dx}(e^{0.5x})
derivative of (4x^3-5x^2/(3x^2-4))	\frac{d}{dx}(\frac{4x^{3}-5x^{2}}{3x^{2}-4})
integral from-1 to 1 of (20-12x)^{-1}	\int\:_{-1}^{1}(20-12x)^{-1}dx
integral of ((sin(2x)))/(e^x)	\int\:\frac{(\sin(2x))}{e^{x}}dx
integral of ((x^2+5x+1))/((x^2+1)^2)	\int\:\frac{(x^{2}+5x+1)}{(x^{2}+1)^{2}}dx
expand x(4-x)^3	expand\:x(4-x)^{3}
d/(dt)(e^{t^3})	\frac{d}{dt}(e^{t^{3}})
derivative of y= 4/x+sqrt(x+0.5)-5x	derivative\:y=\frac{4}{x}+\sqrt{x+0.5}-5x
limit as t approaches 0 of (sin^2(3t))/t	\lim\:_{t\to\:0}(\frac{\sin^{2}(3t)}{t})
(\partial)/(\partial y)(1/(x^2+y^2+z^2))	\frac{\partial\:}{\partial\:y}(\frac{1}{x^{2}+y^{2}+z^{2}})
derivative of 2-tan(x)	\frac{d}{dx}(2-\tan(x))
integral of (log_{e}(x))/(sqrt(x))	\int\:\frac{\log_{e}(x)}{\sqrt{x}}dx
(\partial)/(\partial x)(sqrt(17-x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{17-x^{2}-y^{2}})
derivative of 3/(8(1+x^{5/2)})	\frac{d}{dx}(\frac{3}{8(1+x)^{\frac{5}{2}}})
sum from n=1 to infinity of 5/(10^n)	\sum\:_{n=1}^{\infty\:}\frac{5}{10^{n}}
derivative of y=14sqrt(x)	derivative\:y=14\sqrt{x}
integral of 12tan^{11}(x)sec^2(x)	\int\:12\tan^{11}(x)\sec^{2}(x)dx
integral from 1 to 5 of (x^2+2)/(6x-x^2)	\int\:_{1}^{5}\frac{x^{2}+2}{6x-x^{2}}dx
integral of sqrt(3x^2+4x+1)	\int\:\sqrt{3x^{2}+4x+1}dx
3(dy)/(dx)+15y=5	3\frac{dy}{dx}+15y=5
limit as x approaches 0 of 1+e^x	\lim\:_{x\to\:0}(1+e^{x})
inverse oflaplace ((s+3))/(s^2+3s+2)	inverselaplace\:\frac{(s+3)}{s^{2}+3s+2}
area y^2-2x=2,x-y=3	area\:y^{2}-2x=2,x-y=3
integral of 2/(x-1)	\int\:\frac{2}{x-1}dx
integral of (4x+6)/(sqrt(x^2+3x+1))	\int\:\frac{4x+6}{\sqrt{x^{2}+3x+1}}dx
derivative of y=((2x^2+7))/(x^2+3)	derivative\:y=\frac{(2x^{2}+7)}{x^{2}+3}
limit as x approaches 3pi+of csc(x)	\lim\:_{x\to\:3π+}(\csc(x))
f(x)=-5/(x^2)	f(x)=-\frac{5}{x^{2}}
4sqrt(xy)((dy)/(dx))=1	4\sqrt{xy}(\frac{dy}{dx})=1
integral of 5/(4x^2-49)	\int\:\frac{5}{4x^{2}-49}dx
integral from 6 to 8 of (26)/((x-6)^3)	\int\:_{6}^{8}\frac{26}{(x-6)^{3}}dx
(\partial)/(\partial x)(-4xy(3-x-y))	\frac{\partial\:}{\partial\:x}(-4xy(3-x-y))
y^{''}+2y^'+37y=5e^{-t}cos(6t)	y^{\prime\:\prime\:}+2y^{\prime\:}+37y=5e^{-t}\cos(6t)
integral of e^{ax}sin(0x)	\int\:e^{ax}\sin(0x)dx
f(x)=8x-3	f(x)=8x-3
area x=9y^2,x=4+5y^2	area\:x=9y^{2},x=4+5y^{2}
derivative of f(x)=(3x+4)/(2x+1)	derivative\:f(x)=\frac{3x+4}{2x+1}
limit as z approaches-3 of (z^2-9)/(z+3)	\lim\:_{z\to\:-3}(\frac{z^{2}-9}{z+3})
integral of sec^6(7x)	\int\:\sec^{6}(7x)dx
y^'=0.0012y(1900-y)	y^{\prime\:}=0.0012y(1900-y)
(\partial)/(\partial x)(x^3+y^3+z^3-3xyz)	\frac{\partial\:}{\partial\:x}(x^{3}+y^{3}+z^{3}-3xyz)
implicit (dy)/(dx),y^{2/3}-x^2+xy=1	implicit\:\frac{dy}{dx},y^{\frac{2}{3}}-x^{2}+xy=1
(\partial)/(\partial x)(5xsin(3x^2y))	\frac{\partial\:}{\partial\:x}(5x\sin(3x^{2}y))
derivative of sin^{ln(x}(x))	\frac{d}{dx}(\sin^{\ln(x)}(x))
limit as x approaches 2 of 5x+1	\lim\:_{x\to\:2}(5x+1)
(\partial)/(\partial y)((x^2+y^2)^{4/5})	\frac{\partial\:}{\partial\:y}((x^{2}+y^{2})^{\frac{4}{5}})
tangent of f(x)=sqrt(x^2-x+13),\at x=4	tangent\:f(x)=\sqrt{x^{2}-x+13},\at\:x=4
derivative of f(x)=-4/3 x^{2/3}	derivative\:f(x)=-\frac{4}{3}x^{\frac{2}{3}}
(y^2+1)dx=y*sec^2(x)dy	(y^{2}+1)dx=y\cdot\:\sec^{2}(x)dy
derivative of f(x)=(x^2)/(3+x)	derivative\:f(x)=\frac{x^{2}}{3+x}
y^'+1/x y=8x^2	y^{\prime\:}+\frac{1}{x}y=8x^{2}
derivative of arctan(sqrt(x+1))	\frac{d}{dx}(\arctan(\sqrt{x+1}))
integral of (x^2)/(x^3)+5	\int\:\frac{x^{2}}{x^{3}}+5dx
derivative of r/(sqrt(r^2+3))	derivative\:\frac{r}{\sqrt{r^{2}+3}}
integral of xe^xcos(x)	\int\:xe^{x}\cos(x)dx
laplacetransform 8sin(t)	laplacetransform\:8\sin(t)
sum from k=1 to infinity of (k^3)/(5^k)	\sum\:_{k=1}^{\infty\:}\frac{k^{3}}{5^{k}}
integral of (7sin(x)+2sec(x))/(tan(x))	\int\:\frac{7\sin(x)+2\sec(x)}{\tan(x)}dx
f^'(x)=22x+ln(22x)	f^{\prime\:}(x)=22x+\ln(22x)
inverse oflaplace s/(2s+4)	inverselaplace\:\frac{s}{2s+4}
(\partial)/(\partial x)(5/(xy)+x/y+y/x)	\frac{\partial\:}{\partial\:x}(\frac{5}{xy}+\frac{x}{y}+\frac{y}{x})
(\partial)/(\partial x)(8+xln(xy-7))	\frac{\partial\:}{\partial\:x}(8+x\ln(xy-7))
derivative of 3^{x/2}	\frac{d}{dx}(3^{\frac{x}{2}})
derivative of x^3+x^2-5x	\frac{d}{dx}(x^{3}+x^{2}-5x)
integral of x*e^{5x}	\int\:x\cdot\:e^{5x}dx
integral of (1/(x^2)-1)	\int\:(\frac{1}{x^{2}}-1)dx
limit as x approaches 0 of (5sin(x))/x	\lim\:_{x\to\:0}(\frac{5\sin(x)}{x})
integral of (x-1)^2(x-2)(x-4)	\int\:(x-1)^{2}(x-2)(x-4)dx
derivative of x^2-7x	derivative\:x^{2}-7x
(\partial)/(\partial x)((7x)/(4+x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{7x}{4+x^{2}+y^{2}})
(log_{10}(1+x))^'	(\log_{10}(1+x))^{\prime\:}
laplacetransform-8x	laplacetransform\:-8x
integral of sin(x)-sin^3(x)	\int\:\sin(x)-\sin^{3}(x)dx
integral of arctan(x/4)	\int\:\arctan(\frac{x}{4})dx
integral of ((x^2+2x+1)/(x^2))	\int\:(\frac{x^{2}+2x+1}{x^{2}})dx
integral of 3sin(t)	\int\:3\sin(t)dt
integral of x*(sin(x))^2	\int\:x\cdot\:(\sin(x))^{2}dx
integral of 3sin^2(t)	\int\:3\sin^{2}(t)dt
y^{'''}+6y^{''}+11y^'+6y=0	y^{\prime\:\prime\:\prime\:}+6y^{\prime\:\prime\:}+11y^{\prime\:}+6y=0
integral of (e^{2x}+e^{4x})/(e^x-e^{5x)}	\int\:\frac{e^{2x}+e^{4x}}{e^{x}-e^{5x}}dx
(9y^2-xy)dx+(x^2)dy=0	(9y^{2}-xy)dx+(x^{2})dy=0
integral from 1 to 7 of 1/(x-2)	\int\:_{1}^{7}\frac{1}{x-2}dx
integral of (x^3)/(x^2+9)	\int\:\frac{x^{3}}{x^{2}+9}dx
derivative of 4^{-3}(2/(s^7)+3s)^4	derivative\:4^{-3}(\frac{2}{s^{7}}+3s)^{4}
sum from n=0 to infinity of 1/2 (1/2)^n	\sum\:_{n=0}^{\infty\:}\frac{1}{2}(\frac{1}{2})^{n}
integral of (2x+3)/(x^2+1)	\int\:\frac{2x+3}{x^{2}+1}dx
limit as x approaches 4-of sqrt(16-x^2)	\lim\:_{x\to\:4-}(\sqrt{16-x^{2}})
implicit (dy)/(dx),1=(y/x)	implicit\:\frac{dy}{dx},1=(\frac{y}{x})
derivative of f(x)=8cos(t)	derivative\:f(x)=8\cos(t)

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