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Popular Calculus Problems

integral of 1/((x-3)^{3/2)}	\int\:\frac{1}{(x-3)^{\frac{3}{2}}}dx
limit as x approaches 0 of (2x+1)/(x^3)	\lim\:_{x\to\:0}(\frac{2x+1}{x^{3}})
derivative of e^{e^x+x}	derivative\:e^{e^{x}+x}
derivative of 4/(2x+3)	derivative\:\frac{4}{2x+3}
integral of (x^3)/(\sqrt[5]{x^2+3)}	\int\:\frac{x^{3}}{\sqrt[5]{x^{2}+3}}dx
integral of 1/((x^2+25)^3)	\int\:\frac{1}{(x^{2}+25)^{3}}dx
(\partial)/(\partial x)((3x^2+5x+1)^{3/2})	\frac{\partial\:}{\partial\:x}((3x^{2}+5x+1)^{\frac{3}{2}})
integral of xsqrt(5/2x^2+7)	\int\:x\cdot\:\sqrt{\frac{5}{2}\cdot\:x^{2}+7}dx
integral from 1 to 2 of 3x^2+2x+1	\int\:_{1}^{2}3x^{2}+2x+1dx
integral from 0 to 2 of 2^{-x}	\int\:_{0}^{2}2^{-x}dx
(\partial)/(\partial y)(1/(x^2+y))	\frac{\partial\:}{\partial\:y}(\frac{1}{x^{2}+y})
y^2y^'=y^3-3x,y(0)=2	y^{2}y^{\prime\:}=y^{3}-3x,y(0)=2
limit as x approaches 0 of 2(1+3x)^{2/x}	\lim\:_{x\to\:0}(2(1+3x)^{\frac{2}{x}})
limit as x approaches 8 of x^{4/3}	\lim\:_{x\to\:8}(x^{\frac{4}{3}})
derivative of (3x^2+2x/(4x-2))	\frac{d}{dx}(\frac{3x^{2}+2x}{4x-2})
maclaurin ln(3+x)	maclaurin\:\ln(3+x)
integral of 1/(x^2sqrt(x^2-25))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-25}}dx
derivative of (1+7x^2(x-x^2))	\frac{d}{dx}((1+7x^{2})(x-x^{2}))
derivative of f(x)=3sin(x)+3cos(x)	derivative\:f(x)=3\sin(x)+3\cos(x)
slope of (-4,8),(-3,8)	slope\:(-4,8),(-3,8)
derivative of f(x)=2xe^{7x}	derivative\:f(x)=2xe^{7x}
f(y)=sqrt(1-y^2)	f(y)=\sqrt{1-y^{2}}
derivative of sin(1/(x^2))	derivative\:\sin(\frac{1}{x^{2}})
f^{''}(x)=9x^3+4x^2+7x	f^{\prime\:\prime\:}(x)=9x^{3}+4x^{2}+7x
limit as x approaches 0 of \|x-2\|+3	\lim\:_{x\to\:0}(\left\|x-2\right\|+3)
(\partial)/(\partial y)(sin(y)cos(y))	\frac{\partial\:}{\partial\:y}(\sin(y)\cos(y))
area y=12-x^2,y=-3x-16	area\:y=12-x^{2},y=-3x-16
(e^{2x}*2)^'	(e^{2x}\cdot\:2)^{\prime\:}
derivative of y(θ)=θcos(θ)	derivative\:y(θ)=θ\cos(θ)
derivative of 6xsin(x^2)	derivative\:6x\sin(x^{2})
area y=1-x^2,y=x^2-1	area\:y=1-x^{2},y=x^{2}-1
y^{''}+3y^'-12y=0	y^{\prime\:\prime\:}+3y^{\prime\:}-12y=0
derivative of y=(-13)/(\sqrt[3]{x)}	derivative\:y=\frac{-13}{\sqrt[3]{x}}
integral of sqrt(x)sin(x^{3/2}+1)	\int\:\sqrt{x}\sin(x^{\frac{3}{2}}+1)dx
tangent of 1/(x+3)	tangent\:\frac{1}{x+3}
derivative of sqrt(x)(x^3-5x^2+1)	\frac{d}{dx}(\sqrt{x}(x^{3}-5x^{2}+1))
(\partial)/(\partial x)(xy^3-x^2y)	\frac{\partial\:}{\partial\:x}(xy^{3}-x^{2}y)
derivative of inx	\frac{d}{dx}(inx)
derivative of (x(x+2y)/(1000000))	\frac{d}{dx}(\frac{x(x+2y)}{1000000})
derivative of y= t/((t-9)^2)	derivative\:y=\frac{t}{(t-9)^{2}}
integral of ((sqrt(5x))/5+5/(sqrt(5x)))	\int\:(\frac{\sqrt{5x}}{5}+\frac{5}{\sqrt{5x}})dx
y^{''}+y^'-12y=3e^{2x}	y^{\prime\:\prime\:}+y^{\prime\:}-12y=3e^{2x}
y^{''}+6y^'+8y=-6te^{4t}	y^{\prime\:\prime\:}+6y^{\prime\:}+8y=-6te^{4t}
integral from 1 to 2 of 1/(x(x-5))	\int\:_{1}^{2}\frac{1}{x(x-5)}dx
integral of 1/(xsqrt(2+9x^2))	\int\:\frac{1}{x\sqrt{2+9x^{2}}}dx
derivative of f(x)=(2x+5)/(sqrt(x))	derivative\:f(x)=\frac{2x+5}{\sqrt{x}}
derivative of 4x^{3/4}	\frac{d}{dx}(4x^{\frac{3}{4}})
integral of θarcsec(9θ)	\int\:θ\arcsec(9θ)dθ
derivative of F(r)= 4/(r^3)	derivative\:F(r)=\frac{4}{r^{3}}
(\partial)/(\partial x)(x^8+y^9+z^3-9xyz)	\frac{\partial\:}{\partial\:x}(x^{8}+y^{9}+z^{3}-9xyz)
x^3y^{'''}+xy^'-y=x^2	x^{3}y^{\prime\:\prime\:\prime\:}+xy^{\prime\:}-y=x^{2}
integral of 20x^3(5x^4+6)^3	\int\:20x^{3}(5x^{4}+6)^{3}dx
limit as x approaches 4-of x/(sqrt(x)-2)	\lim\:_{x\to\:4-}(\frac{x}{\sqrt{x}-2})
area 1/x ,1,33	area\:\frac{1}{x},1,33
integral of (42x^2)/(x^4-29x^2+100)	\int\:\frac{42x^{2}}{x^{4}-29x^{2}+100}dx
implicit x^2+8y^2=8	implicit\:x^{2}+8y^{2}=8
integral from 0 to 3 of 1/((x+2)^4)	\int\:_{0}^{3}\frac{1}{(x+2)^{4}}dx
limit as t approaches 0 of (e^{-2t}-1)/t	\lim\:_{t\to\:0}(\frac{e^{-2t}-1}{t})
(\partial)/(\partial x)(sin(x)y^2)	\frac{\partial\:}{\partial\:x}(\sin(x)y^{2})
integral of 1/(2t^3)	\int\:\frac{1}{2t^{3}}dt
derivative of 3x^2y^3	\frac{d}{dx}(3x^{2}y^{3})
derivative of x^2(2x-1^4)	\frac{d}{dx}(x^{2}(2x-1)^{4})
derivative of 2^{5x}	\frac{d}{dx}(2^{5x})
tangent of f(x)=-7-x^2,\at x=9	tangent\:f(x)=-7-x^{2},\at\:x=9
derivative of (xcos(x-2pi)/(x-2pi))	\frac{d}{dx}(\frac{x\cos(x)-2π}{x-2π})
derivative of (1-cos(x)/(1-sin(x)))	\frac{d}{dx}(\frac{1-\cos(x)}{1-\sin(x)})
derivative of (3x^2+1^4)	\frac{d}{dx}((3x^{2}+1)^{4})
sum from k=1 to infinity of (k^3)/(3^k)	\sum\:_{k=1}^{\infty\:}\frac{k^{3}}{3^{k}}
y^'+3y=2e^{-3x}	y^{\prime\:}+3y=2e^{-3x}
tangent of y=x^3-x,(-1,0)	tangent\:y=x^{3}-x,(-1,0)
tangent of f(x)= 2/x ,\at x=-1	tangent\:f(x)=\frac{2}{x},\at\:x=-1
1/x dy-y/(x^2)dx=0	\frac{1}{x}dy-\frac{y}{x^{2}}dx=0
sum from n=1 to infinity of (2/7)^n	\sum\:_{n=1}^{\infty\:}(\frac{2}{7})^{n}
y^'=(-2x)/y	y^{\prime\:}=\frac{-2x}{y}
derivative of-2x^5+1/(2x^2)	\frac{d}{dx}(-2x^{5}+\frac{1}{2x^{2}})
y^{''}+25y=-50sin(5t)	y^{\prime\:\prime\:}+25y=-50\sin(5t)
derivative of 1-(1+x/(200)e^{-x/(200)})	\frac{d}{dx}(1-(1+\frac{x}{200})e^{-\frac{x}{200}})
integral from 0 to 3pi of sin(x)	\int\:_{0}^{3π}\sin(x)dx
taylor 1/(5+7x)	taylor\:\frac{1}{5+7x}
integral of (cos^2(x))/(4+sin(2x))	\int\:\frac{\cos^{2}(x)}{4+\sin(2x)}dx
derivative of 2x^3-9x^2+12x	\frac{d}{dx}(2x^{3}-9x^{2}+12x)
integral from 1 to 2 of (x^2+1)/x	\int\:_{1}^{2}\frac{x^{2}+1}{x}dx
ty^'+ty=1-y	ty^{\prime\:}+ty=1-y
integral of 20t	\int\:20tdt
limit as x approaches 0 of (2x+1)/(2x-2)	\lim\:_{x\to\:0}(\frac{2x+1}{2x-2})
integral of xsec(x)tan(x)	\int\:x\sec(x)\tan(x)dx
taylor 1/(2+z)	taylor\:\frac{1}{2+z}
sum from n=0 to infinity of (-7/8)^n	\sum\:_{n=0}^{\infty\:}(-\frac{7}{8})^{n}
tangent of f(x)=sqrt(5x),(5,5)	tangent\:f(x)=\sqrt{5x},(5,5)
limit as x approaches 2 of [x^2f(x)]	\lim\:_{x\to\:2}([x^{2}f(x)])
tangent of f(x)=-3x^2,\at x=1	tangent\:f(x)=-3x^{2},\at\:x=1
tangent of 5x^3-3x^5	tangent\:5x^{3}-3x^{5}
(xy^2)(dy)/(dx)=y^3-x^3	(xy^{2})\frac{dy}{dx}=y^{3}-x^{3}
integral of x^2sqrt(x-2)	\int\:x^{2}\sqrt{x-2}dx
integral from 1 to 4 of-9sqrt(t)ln(t)	\int\:_{1}^{4}-9\sqrt{t}\ln(t)dt
limit as x approaches 0-of (x+16)/x	\lim\:_{x\to\:0-}(\frac{x+16}{x})
derivative of y=(4x^2-6x)e^x	derivative\:y=(4x^{2}-6x)e^{x}
integral of (2x+3)/(x(x^2-4)(x+2)^2)	\int\:\frac{2x+3}{x(x^{2}-4)(x+2)^{2}}dx
integral of 2sin(6x)	\int\:2\sin(6x)dx
derivative of 25x	\frac{d}{dx}(25x)

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