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Popular Calculus Problems

integral of 1/(sqrt(256+x^2))	\int\:\frac{1}{\sqrt{256+x^{2}}}dx
derivative of e^{xcos(2x)}	derivative\:e^{x\cos(2x)}
(dr)/(dθ)=(r^2+9rθ^2)/(3θ^3)	\frac{dr}{dθ}=\frac{r^{2}+9rθ^{2}}{3θ^{3}}
integral from 0 to 1 of 9cos(3x)	\int\:_{0}^{1}9\cos(3x)dx
integral of 1/((x+3)sqrt(x^2+6x))	\int\:\frac{1}{(x+3)\sqrt{x^{2}+6x}}dx
derivative of f(x)= x/7-1	derivative\:f(x)=\frac{x}{7}-1
integral of (3x-2)/(x^2-x-3)	\int\:\frac{3x-2}{x^{2}-x-3}dx
integral of sqrt(14x-x^2)	\int\:\sqrt{14x-x^{2}}dx
derivative of x^{(-2/5})	\frac{d}{dx}(x^{\frac{-2}{5}})
f(x)=2xcos(x^2)	f(x)=2x\cos(x^{2})
integral from 0 to 2 of 7/(x-2)	\int\:_{0}^{2}\frac{7}{x-2}dx
sum from k=1 to infinity of ln(k)	\sum\:_{k=1}^{\infty\:}\ln(k)
tangent of f(x)=arcsin(3x),\at x= 1/6	tangent\:f(x)=\arcsin(3x),\at\:x=\frac{1}{6}
integral of sqrt(1+(2x-1/(8x))^2)	\int\:\sqrt{1+(2x-\frac{1}{8x})^{2}}dx
integral from-3 to 1 of (1+2x)	\int\:_{-3}^{1}(1+2x)dx
(e^{12x})^'	(e^{12x})^{\prime\:}
integral of sinh^2(x)cosh(x)	\int\:\sinh^{2}(x)\cosh(x)dx
limit as x approaches 0 of xcos(1/(x^2))	\lim\:_{x\to\:0}(x\cos(\frac{1}{x^{2}}))
integral of (1-x^3)^2x	\int\:(1-x^{3})^{2}xdx
integral of xe^{-5x^2}	\int\:xe^{-5x^{2}}dx
integral of (2x+4)(x^2+4x+10)^4	\int\:(2x+4)(x^{2}+4x+10)^{4}dx
integral of x^5sqrt(x^3+3)	\int\:x^{5}\sqrt{x^{3}+3}dx
integral from 0 to 1 of 2x^4e^{-x}	\int\:_{0}^{1}2x^{4}e^{-x}dx
slope of y=(x^2-3)^4,\at x=2	slope\:y=(x^{2}-3)^{4},\at\:x=2
derivative of x^{x/2}	\frac{d}{dx}(x^{\frac{x}{2}})
integral of (ln(x^3))/(ln(x^2))	\int\:\frac{\ln(x^{3})}{\ln(x^{2})}dx
integral of (4x+7)sin(4x)	\int\:(4x+7)\sin(4x)dx
integral of sin(2x)x^2	\int\:\sin(2x)x^{2}dx
integral from 0 to 4 of 2pix(sqrt(x))	\int\:_{0}^{4}2πx(\sqrt{x})dx
integral of (\sqrt[6]{x})^3	\int\:(\sqrt[6]{x})^{3}dx
sum from n=1 to infinity of 4^n*x^n	\sum\:_{n=1}^{\infty\:}4^{n}\cdot\:x^{n}
sum from n=1 to infinity of 1/(3n+1)	\sum\:_{n=1}^{\infty\:}\frac{1}{3n+1}
derivative of csc(x^2)	\frac{d}{dx}(\csc(x^{2}))
integral of sin(-5x^4-x-6)(-20x^3-1)	\int\:\sin(-5x^{4}-x-6)(-20x^{3}-1)dx
area f(x)=x^2,g(x)=sqrt(9+x)	area\:f(x)=x^{2},g(x)=\sqrt{9+x}
integral of y/(y^2+2)	\int\:\frac{y}{y^{2}+2}dy
integral of (10x-3)	\int\:(10x-3)dx
area x^2-3x+2,-3x+3	area\:x^{2}-3x+2,-3x+3
derivative of ((sqrt(t)-3t))/t	derivative\:\frac{(\sqrt{t}-3t)}{t}
(\partial)/(\partial x)((3xy)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{3xy}{x^{2}+y^{2}})
taylor e^{-7x},0	taylor\:e^{-7x},0
integral of arctan^2(x)	\int\:\arctan^{2}(x)dx
derivative of cos^4(x+sin^4(x))	\frac{d}{dx}(\cos^{4}(x)+\sin^{4}(x))
limit as x approaches 3+of 3/(x-3)	\lim\:_{x\to\:3+}(\frac{3}{x-3})
derivative of (2x^{1/2})	\frac{d}{dx}((2x)^{\frac{1}{2}})
derivative of cos(x^2e^x)	\frac{d}{dx}(\cos(x^{2}e^{x}))
limit as x approaches-2 of-x^2+5x-1	\lim\:_{x\to\:-2}(-x^{2}+5x-1)
inverse oflaplace F(s)=(s^2-2s-6)/(s-2)	inverselaplace\:F(s)=\frac{s^{2}-2s-6}{s-2}
limit as x approaches 3+of (x+2)/(x-2)	\lim\:_{x\to\:3+}(\frac{x+2}{x-2})
derivative of x^{ln(sqrt(x)})	\frac{d}{dx}(x^{\ln(\sqrt{x})})
(dy)/(dx)= y/2	\frac{dy}{dx}=\frac{y}{2}
integral of 4/(x^4)	\int\:\frac{4}{x^{4}}dx
derivative of sqrt(16+x^2)	\frac{d}{dx}(\sqrt{16+x^{2}})
derivative of axcos(3x)	\frac{d}{dx}(ax\cos(3x))
sum from n=1 to infinity of 1/(2^n+3^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{2^{n}+3^{n}}
xy^2((dy)/(dx))=y^3-x^3	xy^{2}(\frac{dy}{dx})=y^{3}-x^{3}
integral of (2xy^2+2y)	\int\:(2xy^{2}+2y)dx
xy^'+2y=3x	xy^{\prime\:}+2y=3x
area y=2-x^2,y=-x	area\:y=2-x^{2},y=-x
simplify x-y	simplify\:x-y
laplacetransform 3cos(6t)	laplacetransform\:3\cos(6t)
derivative of (sqrt(x))/(x+9)	derivative\:\frac{\sqrt{x}}{x+9}
sum from n=4 to infinity of (1/2)^n	\sum\:_{n=4}^{\infty\:}(\frac{1}{2})^{n}
integral of 1/(-e^{3x)}	\int\:\frac{1}{-e^{3x}}dx
integral from 0 to infinity of 1/(e^x)	\int\:_{0}^{\infty\:}\frac{1}{e^{x}}dx
derivative of 2e^x-3x^2sqrt(x)	\frac{d}{dx}(2e^{x}-3x^{2}\sqrt{x})
integral from 0 to 5 of x/(sqrt(x+4))	\int\:_{0}^{5}\frac{x}{\sqrt{x+4}}dx
integral of 1/(1+t^3)	\int\:\frac{1}{1+t^{3}}dt
integral of 1/(7^x)	\int\:\frac{1}{7^{x}}dx
tangent of f(x)=-x^2+7x	tangent\:f(x)=-x^{2}+7x
integral from-1 to 1 of x^3-6x	\int\:_{-1}^{1}x^{3}-6xdx
tangent of x^4+5x^2-x	tangent\:x^{4}+5x^{2}-x
derivative of h(w)=(w^2-1)/(w^2+1)	derivative\:h(w)=\frac{w^{2}-1}{w^{2}+1}
derivative of (x^3/(12))	\frac{d}{dx}(\frac{x^{3}}{12})
derivative of 1/2 (9t^2+t)^{-3}	derivative\:\frac{1}{2}(9t^{2}+t)^{-3}
integral from 0 to 1 of x^2+sqrt(x)	\int\:_{0}^{1}x^{2}+\sqrt{x}dx
y^{''}+y=0,y(0)=0	y^{\prime\:\prime\:}+y=0,y(0)=0
d/(d{r)}(sqrt(4-{r)^2})	\frac{d}{d{r}}(\sqrt{4-{r}^{2}})
integral of x(3sec^2(x)+2tan^2(x))	\int\:x(3\sec^{2}(x)+2\tan^{2}(x))dx
tangent of y=7\sqrt[4]{x^3}	tangent\:y=7\sqrt[4]{x^{3}}
3y^{''}+2y=x^2e^{-3x}	3y^{\prime\:\prime\:}+2y=x^{2}e^{-3x}
derivative of (x^2/(x^2+x+1))	\frac{d}{dx}(\frac{x^{2}}{x^{2}+x+1})
tangent of y=ln(1-x^2+2x^4),\at x=1	tangent\:y=\ln(1-x^{2}+2x^{4}),\at\:x=1
d/(dy)(x^2+y^2)	\frac{d}{dy}(x^{2}+y^{2})
sum from n=1 to infinity of n^2(-1)^n	\sum\:_{n=1}^{\infty\:}n^{2}(-1)^{n}
tangent of f(x)=x^2+x,(-3,1)	tangent\:f(x)=x^{2}+x,(-3,1)
derivative of f(x)=(e^x)/(4x^2+1)	derivative\:f(x)=\frac{e^{x}}{4x^{2}+1}
integral of 1/(x(a^2-x^2))	\int\:\frac{1}{x(a^{2}-x^{2})}dx
integral of 1/(4+9x^2)	\int\:\frac{1}{4+9x^{2}}dx
slope of y=8x-x^2(1.7)	slope\:y=8x-x^{2}(1.7)
limit as x approaches 0 of e^x+1/x	\lim\:_{x\to\:0}(e^{x}+\frac{1}{x})
derivative of 0.8x^{1.3}	\frac{d}{dx}(0.8x^{1.3})
limit as x approaches 3-of-x+5	\lim\:_{x\to\:3-}(-x+5)
limit as t approaches 0 of cos(2t)k	\lim\:_{t\to\:0}(\cos(2t)k)
integral of (x+2)ln((x+2)^2)	\int\:(x+2)\ln((x+2)^{2})dx
integral of 2021	\int\:2021
integral of x(x-2)(x-3)(x+2)(x+3)	\int\:x(x-2)(x-3)(x+2)(x+3)dx
limit as x approaches-9 of-8	\lim\:_{x\to\:-9}(-8)
derivative of x*ln(x^2)	\frac{d}{dx}(x\cdot\:\ln(x^{2}))
(\partial)/(\partial x)((xz)/(y+z))	\frac{\partial\:}{\partial\:x}(\frac{xz}{y+z})

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