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Popular Calculus Problems

sum from n=1 to infinity of \sqrt[5]{(32)/(n^6)}	\sum\:_{n=1}^{\infty\:}\sqrt[5]{\frac{32}{n^{6}}}
derivative of f(x)=(x^2+1)(2-x)	derivative\:f(x)=(x^{2}+1)(2-x)
limit as x approaches-3 of sqrt(2x+5)	\lim\:_{x\to\:-3}(\sqrt{2x+5})
derivative of cos(x^{-6})	\frac{d}{dx}(\cos(x^{-6}))
tangent of f(x)=8e^x+x,\at x=0	tangent\:f(x)=8e^{x}+x,\at\:x=0
integral of (x+1)e^{3x+1}	\int\:(x+1)e^{3x+1}dx
integral of 5x^4-2x^5	\int\:5x^{4}-2x^{5}dx
inverse oflaplace 6s	inverselaplace\:6s
integral of 4cos(x^2)	\int\:4\cos(x^{2})dx
(tan(x)-sin(x)sin(y))dx+cos(x)cos(y)dy=0	(\tan(x)-\sin(x)\sin(y))dx+\cos(x)\cos(y)dy=0
xy^'-x-x^2-3y=0	xy^{\prime\:}-x-x^{2}-3y=0
integral of (3t^2)/(sqrt(t^3+5))	\int\:\frac{3t^{2}}{\sqrt{t^{3}+5}}dt
integral of x*sqrt(x+3)	\int\:x\cdot\:\sqrt{x+3}dx
(\partial)/(\partial y)(x+ysin(t))	\frac{\partial\:}{\partial\:y}(x+y\sin(t))
integral from 0 to pi of sin^2(xco)s^4x	\int\:_{0}^{π}\sin^{2}(xco)s^{4}xdx
integral of (sec^2(x)+2)	\int\:(\sec^{2}(x)+2)dx
limit as x approaches-7+of (x-4)/(x+7)	\lim\:_{x\to\:-7+}(\frac{x-4}{x+7})
(\partial)/(\partial x)(7+8xsqrt(y))	\frac{\partial\:}{\partial\:x}(7+8x\sqrt{y})
limit as x approaches 0 of 1/(sqrt(2x))	\lim\:_{x\to\:0}(\frac{1}{\sqrt{2x}})
derivative of 5x-e	\frac{d}{dx}(5x-e)
(\partial)/(\partial x)((6x-7y)/(y^2+x^2))	\frac{\partial\:}{\partial\:x}(\frac{6x-7y}{y^{2}+x^{2}})
xy^'=y+x^2sin(x),y(pi/6)=0	xy^{\prime\:}=y+x^{2}\sin(x),y(\frac{π}{6})=0
derivative of ((x^2+2/(x^3-1))^3)	\frac{d}{dx}((\frac{x^{2}+2}{x^{3}-1})^{3})
inverse oflaplace 1/(s^3(s^2+1))	inverselaplace\:\frac{1}{s^{3}(s^{2}+1)}
derivative of 3x^2ln(x+x^2)	\frac{d}{dx}(3x^{2}\ln(x)+x^{2})
integral of e^{-21x}	\int\:e^{-21x}dx
integral of 1/(x^4-x^3)	\int\:\frac{1}{x^{4}-x^{3}}dx
laplacetransform cos(3x)	laplacetransform\:\cos(3x)
derivative of (10/(ln(x)))	\frac{d}{dx}(\frac{10}{\ln(x)})
t^2(dy)/(dt)+y=0,y(7)=-4	t^{2}\frac{dy}{dt}+y=0,y(7)=-4
integral of sin(2t)(cot(2t)+1)	\int\:\sin(2t)(\cot(2t)+1)dt
derivative of \|x-1\|^3	\frac{d}{dx}(\left\|x-1\right\|^{3})
limit as x approaches 0 of \|x-1\|	\lim\:_{x\to\:0}(\left\|x-1\right\|)
limit as x approaches 5 of 2xsqrt(5)	\lim\:_{x\to\:5}(2x\sqrt{5})
(\partial)/(\partial x)(e^{2x}*2)	\frac{\partial\:}{\partial\:x}(e^{2x}\cdot\:2)
derivative of f(x)=(2x-7)^4(x^2+x+1)^5	derivative\:f(x)=(2x-7)^{4}(x^{2}+x+1)^{5}
integral of (1+x^2)/(x^3)	\int\:\frac{1+x^{2}}{x^{3}}dx
(\partial)/(\partial x)(2-sqrt(y-x^2))	\frac{\partial\:}{\partial\:x}(2-\sqrt{y-x^{2}})
taylor cos(x/2)	taylor\:\cos(\frac{x}{2})
integral of 1/(e^{5x)}	\int\:\frac{1}{e^{5x}}dx
integral of-7x^{-8}	\int\:-7x^{-8}dx
derivative of y=5csc(x)+7cos(x)	derivative\:y=5\csc(x)+7\cos(x)
integral of (x^2-10x+4)/(x^3)	\int\:\frac{x^{2}-10x+4}{x^{3}}dx
derivative of 2-e^{-x}	\frac{d}{dx}(2-e^{-x})
sum from n=0 to infinity of 1/(2^{2n+1)}	\sum\:_{n=0}^{\infty\:}\frac{1}{2^{2n+1}}
limit as x approaches infinity of 1	\lim\:_{x\to\:\infty\:}(1)
integral of (2t)/(t^2+1)	\int\:\frac{2t}{t^{2}+1}dt
derivative of f(x)=\|2x-3\|	derivative\:f(x)=\left\|2x-3\right\|
f(x)=-sin(x^2)*2x	f(x)=-\sin(x^{2})\cdot\:2x
integral of (x^4-3x^2+x-sqrt(x)+2)/x	\int\:\frac{x^{4}-3x^{2}+x-\sqrt{x}+2}{x}dx
laplacetransform 7+3t	laplacetransform\:7+3t
integral of (x^3)/((1-2x^4)^5)	\int\:\frac{x^{3}}{(1-2x^{4})^{5}}dx
xy^{''}=y^'+(y^')^3	xy^{\prime\:\prime\:}=y^{\prime\:}+(y^{\prime\:})^{3}
limit as x approaches-3-of (4x)/(9-x^2)	\lim\:_{x\to\:-3-}(\frac{4x}{9-x^{2}})
integral of 1/(x^2-x+2)	\int\:\frac{1}{x^{2}-x+2}dx
integral of 1/(x^2(x^2-1))	\int\:\frac{1}{x^{2}(x^{2}-1)}dx
(t^2+16)^2y^'+2t(t^2+16)y=4,y(-2)=10	(t^{2}+16)^{2}y^{\prime\:}+2t(t^{2}+16)y=4,y(-2)=10
integral of ((arctan(x))/(1+x^2))	\int\:(\frac{\arctan(x)}{1+x^{2}})dx
integral of sqrt(36-4x^2)	\int\:\sqrt{36-4x^{2}}dx
integral of 3xe^{-3x}	\int\:3xe^{-3x}dx
integral of e^{-x}sin(4x)	\int\:e^{-x}\sin(4x)dx
(x^2+1)y^'+6x(y-1)=0,y(0)=8	(x^{2}+1)y^{\prime\:}+6x(y-1)=0,y(0)=8
integral of (ln(y))^2	\int\:(\ln(y))^{2}dy
area xsqrt(4-x^2),0	area\:x\sqrt{4-x^{2}},0
simplify sqrt(x)+sqrt(y)	simplify\:\sqrt{x}+\sqrt{y}
area y= 1/x ,x=2,y=-1	area\:y=\frac{1}{x},x=2,y=-1
integral from-infinity to-1 of xe^x	\int\:_{-\infty\:}^{-1}xe^{x}dx
limit as x approaches 6 of 9x+x^2(3x+5)	\lim\:_{x\to\:6}(9x+x^{2}(3x+5))
derivative of y=(2x-1)(3x+4)(x+7)	derivative\:y=(2x-1)(3x+4)(x+7)
integral of sqrt(t)-8cos(t)	\int\:\sqrt{t}-8\cos(t)dt
integral of (x^3-x^2-2x)/(4x-2)	\int\:\frac{x^{3}-x^{2}-2x}{4x-2}dx
limit as x approaches infinity+of (log_{6}(x))/(log_{8)(x)}	\lim\:_{x\to\:\infty\:+}(\frac{\log_{6}(x)}{\log_{8}(x)})
(d^5)/(dx^5)(1/x+cos(2x))	\frac{d^{5}}{dx^{5}}(\frac{1}{x}+\cos(2x))
derivative of 12xy	\frac{d}{dx}(12xy)
derivative of f(x)=(sqrt(x)+x)/(x^2)	derivative\:f(x)=\frac{\sqrt{x}+x}{x^{2}}
derivative of f(x)=e^{(x^2-x)}	derivative\:f(x)=e^{(x^{2}-x)}
integral of e^x-xe^{x^2}	\int\:e^{x}-xe^{x^{2}}dx
derivative of ln(81sin^2(x))	derivative\:\ln(81\sin^{2}(x))
integral of (200)/(20-3x)	\int\:\frac{200}{20-3x}dx
limit as x approaches 1 of x^3+1	\lim\:_{x\to\:1}(x^{3}+1)
limit as x approaches infinity of 5*x	\lim\:_{x\to\:\infty\:}(5\cdot\:x)
integral of 1/((1+x)sqrt(x))	\int\:\frac{1}{(1+x)\sqrt{x}}dx
derivative of \sqrt[3]{x}-4/x	\frac{d}{dx}(\sqrt[3]{x}-\frac{4}{x})
integral from 0 to 1 of 4e^{6sqrt(x)}	\int\:_{0}^{1}4e^{6\sqrt{x}}dx
sum from n=0 to infinity of (3^n)/(n!)	\sum\:_{n=0}^{\infty\:}\frac{3^{n}}{n!}
derivative of (xcos(x)sin(x))	\frac{d}{dx}((x)\cos(x)\sin(x))
(\partial)/(\partial x)(e^{2(2x+y)})	\frac{\partial\:}{\partial\:x}(e^{2(2x+y)})
derivative of ln(x^2-1)	derivative\:\ln(x^{2}-1)
sum from n=0 to infinity of nx^{n-1}	\sum\:_{n=0}^{\infty\:}nx^{n-1}
derivative of x^{(-5/9})	\frac{d}{dx}(x^{\frac{-5}{9}})
derivative of f(x)=e^{-(x^2)/2}	derivative\:f(x)=e^{-\frac{x^{2}}{2}}
integral from 2 to 8 of (-x+10)	\int\:_{2}^{8}(-x+10)dx
sqrt(y)dx+(1+x)dy=0,y(0)=1	\sqrt{y}dx+(1+x)dy=0,y(0)=1
integral of (7/(x^5)+8e^{2x}-4x)	\int\:(\frac{7}{x^{5}}+8e^{2x}-4x)dx
sum from n=1 to infinity of (-2^n)/(n^7)	\sum\:_{n=1}^{\infty\:}\frac{-2^{n}}{n^{7}}
derivative of (12-3y-2x/4)	\frac{d}{dx}(\frac{12-3y-2x}{4})
derivative of y=sqrt(x)(x^2+1)^3	derivative\:y=\sqrt{x}(x^{2}+1)^{3}
integral of (cos(nx))	\int\:(\cos(nx))dx
integral from-1 to 2 of (1-x)	\int\:_{-1}^{2}(1-x)dx
sum from n=1 to infinity of 1/(3^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{3^{n}}

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