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Popular Calculus Problems

derivative of ln(1+sin(2x))	\frac{d}{dx}(\ln(1+\sin(2x)))
integral of (x^3)/(x^3-7x+6)	\int\:\frac{x^{3}}{x^{3}-7x+6}dx
(\partial)/(\partial y)(sin(3x+4y))	\frac{\partial\:}{\partial\:y}(\sin(3x+4y))
integral of (cos(t))/(1+sin(t))	\int\:\frac{\cos(t)}{1+\sin(t)}dt
(\partial)/(\partial x)(x^2ln(x))	\frac{\partial\:}{\partial\:x}(x^{2}\ln(x))
integral of (4x-2)/((x^2-x+1)^7)	\int\:\frac{4x-2}{(x^{2}-x+1)^{7}}dx
f(x)=ln(cos(2x))	f(x)=\ln(\cos(2x))
integral of 8/(sqrt(16-x^2))	\int\:\frac{8}{\sqrt{16-x^{2}}}dx
area y=7-x,x=((y-4)^2)/4	area\:y=7-x,x=\frac{(y-4)^{2}}{4}
integral of (2x+1)e^x	\int\:(2x+1)e^{x}dx
(\partial)/(\partial x)(sqrt(6x+3y))	\frac{\partial\:}{\partial\:x}(\sqrt{6x+3y})
derivative of ln(x^2-3)	\frac{d}{dx}(\ln(x^{2}-3))
tangent of y=2x^4-16x^2+9,\at x=-4	tangent\:y=2x^{4}-16x^{2}+9,\at\:x=-4
tangent of y= 2/x ,(5, 2/5)	tangent\:y=\frac{2}{x},(5,\frac{2}{5})
integral of-2x^{-3}	\int\:-2x^{-3}dx
area y^2=2x,x=2y	area\:y^{2}=2x,x=2y
x^2y^{''}+xy^'-4y=0	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}-4y=0
derivative of cos(x+cot(x)+csc(x)+3e^x)	\frac{d}{dx}(\cos(x)+\cot(x)+\csc(x)+3e^{x})
sum from n=0 to infinity of (2/3)^{-n}	\sum\:_{n=0}^{\infty\:}(\frac{2}{3})^{-n}
derivative of f(x)=(7^x)/(x^3)	derivative\:f(x)=\frac{7^{x}}{x^{3}}
(\partial)/(\partial y)(x^3y^3)	\frac{\partial\:}{\partial\:y}(x^{3}y^{3})
integral from 1 to sqrt(3 of) 1/(1+x^2)	\int\:_{1}^{\sqrt{3}}\frac{1}{1+x^{2}}dx
derivative of arctan(sqrt(3x^2-1))	derivative\:\arctan(\sqrt{3x^{2}-1})
7y^{''}+y^'=0	7y^{\prime\:\prime\:}+y^{\prime\:}=0
sum from n=1 to infinity of 9/(n^2+1)	\sum\:_{n=1}^{\infty\:}\frac{9}{n^{2}+1}
integral from 1 to 16 of 1/(10+sqrt(x))	\int\:_{1}^{16}\frac{1}{10+\sqrt{x}}dx
limit as x approaches 1+of (3+x)/(x^2-1)	\lim\:_{x\to\:1+}(\frac{3+x}{x^{2}-1})
integral from-1 to 1 of (\sqrt[3]{t}-2)	\int\:_{-1}^{1}(\sqrt[3]{t}-2)dt
tangent of f(x)=(4x)/(x^2+1),\at x=-1	tangent\:f(x)=\frac{4x}{x^{2}+1},\at\:x=-1
integral of x/(x^2+3x+3)	\int\:\frac{x}{x^{2}+3x+3}dx
derivative of 8tan^2(8x)	derivative\:8\tan^{2}(8x)
derivative of \|x^2-2x\|	\frac{d}{dx}(\left\|x^{2}-2x\right\|)
integral of 3y^5	\int\:3y^{5}dy
integral from-a to a of f(x)	\int\:_{-a}^{a}f(x)dx
derivative of x^5+37x	\frac{d}{dx}(x^{5}+37x)
limit as x approaches 0 of 1/(1-cos(x))	\lim\:_{x\to\:0}(\frac{1}{1-\cos(x)})
integral of e^{-x^2+3x}	\int\:e^{-x^{2}+3x}dx
laplacetransform e^{-5t}	laplacetransform\:e^{-5t}
(dy)/(dx)=10x	\frac{dy}{dx}=10x
integral of 1/(csc^4(3t)sec^2(3t))	\int\:\frac{1}{\csc^{4}(3t)\sec^{2}(3t)}dt
(\partial)/(\partial y)(x^3-12xy+8y^3)	\frac{\partial\:}{\partial\:y}(x^{3}-12xy+8y^{3})
(\partial)/(\partial x)((e^y)/(e^x+e^y))	\frac{\partial\:}{\partial\:x}(\frac{e^{y}}{e^{x}+e^{y}})
integral of e^{-0.5x^2}	\int\:e^{-0.5x^{2}}dx
(\partial)/(\partial x)(y+x)	\frac{\partial\:}{\partial\:x}(y+x)
integral of 5^{tan(x)}sec^2(x)	\int\:5^{\tan(x)}\sec^{2}(x)dx
(dy)/(dx)=(4x+xy^2)/(y-x^2y)	\frac{dy}{dx}=\frac{4x+xy^{2}}{y-x^{2}y}
derivative of e^{8e^x}*8e^x	derivative\:e^{8e^{x}}\cdot\:8e^{x}
integral of x^{1/2}+cos(x)+5	\int\:x^{\frac{1}{2}}+\cos(x)+5dx
integral of sqrt(x/y)	\int\:\sqrt{\frac{x}{y}}dx
(\partial)/(\partial x)((100)/(4x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{100}{4x^{2}+y^{2}})
derivative of x-2x^2	\frac{d}{dx}(x-2x^{2})
integral of x^2*cos(3x)	\int\:x^{2}\cdot\:\cos(3x)dx
integral of (2x+1)/(e^x)	\int\:\frac{2x+1}{e^{x}}dx
derivative of f(x)=x^2+2/x	derivative\:f(x)=x^{2}+\frac{2}{x}
integral of e^{x^{1/3}}	\int\:e^{x^{\frac{1}{3}}}dx
tangent of f(x)=3x^4-4x^2+1,\at x=-1	tangent\:f(x)=3x^{4}-4x^{2}+1,\at\:x=-1
(x+1)dy-ydx=0	(x+1)dy-ydx=0
limit as x approaches 0 of (2x)/(cos(x))	\lim\:_{x\to\:0}(\frac{2x}{\cos(x)})
limit as x approaches 3 of (1-x)/x	\lim\:_{x\to\:3}(\frac{1-x}{x})
(\partial)/(\partial x)(9/(8x+3y))	\frac{\partial\:}{\partial\:x}(\frac{9}{8x+3y})
integral of x/(1-4x^2)	\int\:\frac{x}{1-4x^{2}}dx
derivative of 2^xlog_{2}(x)	derivative\:2^{x}\log_{2}(x)
integral of (3x-1)/(sqrt(x+1))	\int\:\frac{3x-1}{\sqrt{x+1}}dx
(\partial)/(\partial x)(y-x^2-xy^2)	\frac{\partial\:}{\partial\:x}(y-x^{2}-xy^{2})
integral from 1 to 3 of 3x^2+1/(12x^2)	\int\:_{1}^{3}3x^{2}+\frac{1}{12x^{2}}dx
limit as x approaches 3 of-4	\lim\:_{x\to\:3}(-4)
laplacetransform 13e^{4t}*e^2	laplacetransform\:13e^{4t}\cdot\:e^{2}
integral from 1/2 to 5 of 10xln(2x)	\int\:_{\frac{1}{2}}^{5}10x\ln(2x)dx
derivative of f(x)=5x^{-15}	derivative\:f(x)=5x^{-15}
f(t)=1-cos(t)	f(t)=1-\cos(t)
(xdy)/(dx)+y=e^x	\frac{xdy}{dx}+y=e^{x}
derivative of tan(x+x^4)	\frac{d}{dx}(\tan(x)+x^{4})
integral of arcsin(x)	\int\:\arcsin(x)dx
y^{''}-2y^'+26y=0,y(0)=2,y^'(0)=5	y^{\prime\:\prime\:}-2y^{\prime\:}+26y=0,y(0)=2,y^{\prime\:}(0)=5
(\partial)/(\partial x)(2xln(x^2y))	\frac{\partial\:}{\partial\:x}(2x\ln(x^{2}y))
inverse oflaplace-2/(s^2)	inverselaplace\:-\frac{2}{s^{2}}
integral of 5xlog_{10}(3-x)	\int\:5x\log_{10}(3-x)dx
area sqrt(x),0,1	area\:\sqrt{x},0,1
derivative of ln(2x^3-x^2)	\frac{d}{dx}(\ln(2x^{3}-x^{2}))
derivative of sqrt(5x^3)	\frac{d}{dx}(\sqrt{5x^{3}})
derivative of 4/(3x^3)	\frac{d}{dx}(\frac{4}{3x^{3}})
integral of x^3sqrt(x^2-5)	\int\:x^{3}\sqrt{x^{2}-5}dx
(dy)/(dx)-3/x y=x^3	\frac{dy}{dx}-\frac{3}{x}y=x^{3}
sum from k=1 to infinity of 0	\sum\:_{k=1}^{\infty\:}0
area y=x,x=3,x=6	area\:y=x,x=3,x=6
derivative of x^3+9x^2+35x+14	derivative\:x^{3}+9x^{2}+35x+14
derivative of (x^4)/4+1/(8x^2)	derivative\:\frac{x^{4}}{4}+\frac{1}{8x^{2}}
derivative of sin(x^2-1)	\frac{d}{dx}(\sin(x^{2}-1))
derivative of f(x)=(6x^2+4x+8)/(sqrt(x))	derivative\:f(x)=\frac{6x^{2}+4x+8}{\sqrt{x}}
derivative of x^3-ysinh(x^2)	\frac{d}{dx}(x^{3}-y\sinh(x^{2}))
integral from-1 to 1 of 1/(x^5)	\int\:_{-1}^{1}\frac{1}{x^{5}}dx
(\partial)/(\partial x)(7e^x*sin(y))	\frac{\partial\:}{\partial\:x}(7e^{x}\cdot\:\sin(y))
sum from n=1 to infinity of 1/(2nln(n))	\sum\:_{n=1}^{\infty\:}\frac{1}{2n\ln(n)}
derivative of (4x^2+4x+2/(sqrt(x)))	\frac{d}{dx}(\frac{4x^{2}+4x+2}{\sqrt{x}})
integral from 1 to 3 of 2xe^{-4x}	\int\:_{1}^{3}2xe^{-4x}dx
integral of 3x^2+4x+1	\int\:3x^{2}+4x+1dx
(dy)/(dx)+1/(x+4)y=x^{-2}	\frac{dy}{dx}+\frac{1}{x+4}y=x^{-2}
derivative of f(x)=(9x)/(e^x)	derivative\:f(x)=\frac{9x}{e^{x}}
integral from 0 to 3 of (2x^2-6x)	\int\:_{0}^{3}(2x^{2}-6x)dx
limit as x approaches 0 of 2/x-2/(\|x\|)	\lim\:_{x\to\:0}(\frac{2}{x}-\frac{2}{\left\|x\right\|})

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