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Popular Calculus Problems

integral from 0 to infinity of 3e^{-3x}	\int\:_{0}^{\infty\:}3e^{-3x}dx
derivative of 9/(8\sqrt[4]{x^3})	\frac{d}{dx}(\frac{9}{8\sqrt[4]{x^{3}}})
integral from 0 to 1 of 1/((x-1)^{2/3)}	\int\:_{0}^{1}\frac{1}{(x-1)^{\frac{2}{3}}}dx
derivative of (8x^{1/3})	\frac{d}{dx}((8x)^{\frac{1}{3}})
integral of-cos(t)sin^2(t)	\int\:-\cos(t)\sin^{2}(t)dt
derivative of (e^x/(e^x+5))	\frac{d}{dx}(\frac{e^{x}}{e^{x}+5})
integral of 3cos^2(x)sin(2x)	\int\:3\cos^{2}(x)\sin(2x)dx
derivative of 8sqrt(4x-1)	\frac{d}{dx}(8\sqrt{4x-1})
limit as x approaches 2 of x^2+a	\lim\:_{x\to\:2}(x^{2}+a)
y^{'''}-3y^{''}+3y^'-y=x	y^{\prime\:\prime\:\prime\:}-3y^{\prime\:\prime\:}+3y^{\prime\:}-y=x
derivative of cos(ln(x)+sin(ln(x)))	\frac{d}{dx}(\cos(\ln(x))+\sin(\ln(x)))
integral of (sqrt(x))/2+2/(sqrt(x))	\int\:\frac{\sqrt{x}}{2}+\frac{2}{\sqrt{x}}dx
(\partial)/(\partial x)((x+y)/(xy-1))	\frac{\partial\:}{\partial\:x}(\frac{x+y}{xy-1})
(dy)/(dx)=sin(y)+1	\frac{dy}{dx}=\sin(y)+1
derivative of x^{3cos(x})	\frac{d}{dx}(x^{3\cos(x)})
derivative of f(x)=sqrt(7x)	derivative\:f(x)=\sqrt{7x}
limit as x approaches 8 of (1+\sqrt[3]{x})(x^3-6x^2+2)	\lim\:_{x\to\:8}((1+\sqrt[3]{x})(x^{3}-6x^{2}+2))
(\partial)/(\partial x)(x^2+2x+y^2)	\frac{\partial\:}{\partial\:x}(x^{2}+2x+y^{2})
derivative of f(x)=4x^2-x^3	derivative\:f(x)=4x^{2}-x^{3}
(\partial)/(\partial z)(x/(y+2z))	\frac{\partial\:}{\partial\:z}(\frac{x}{y+2z})
x^{''}+4x=0	x^{\prime\:\prime\:}+4x=0
sum from n=1 to infinity of 1/(n+1^{-n)}	\sum\:_{n=1}^{\infty\:}\frac{1}{n+1^{-n}}
5y^{''}+15y^'-20y=0	5y^{\prime\:\prime\:}+15y^{\prime\:}-20y=0
integral of (x^2-x+1)	\int\:(x^{2}-x+1)dx
integral of 6/(x^2sqrt(x^2+16))	\int\:\frac{6}{x^{2}\sqrt{x^{2}+16}}dx
limit as x approaches 2 of x+1	\lim\:_{x\to\:2}(x+1)
integral from 0 to infinity of sin(2x)	\int\:_{0}^{\infty\:}\sin(2x)dx
limit as x approaches 2 of (3x+1)/(x+2)	\lim\:_{x\to\:2}(\frac{3x+1}{x+2})
d/(dt)(0.00225te^{-0.0467t})	\frac{d}{dt}(0.00225te^{-0.0467t})
(\partial)/(\partial x)(xy(sin((x^5)+y^5)))	\frac{\partial\:}{\partial\:x}(xy(\sin((x^{5})+y^{5})))
integral from-1 to 2 of 1/(x^2)	\int\:_{-1}^{2}\frac{1}{x^{2}}dx
derivative of \|x-2\|	\frac{d}{dx}(\left\|x-2\right\|)
derivative of e^{(3/x)}	derivative\:e^{(\frac{3}{x})}
derivative of (x^5-7^2)	\frac{d}{dx}((x^{5}-7)^{2})
integral of (sin(ln(x)))/x	\int\:\frac{\sin(\ln(x))}{x}dx
integral of (x^2)/((x^2+25)^{3/2)}	\int\:\frac{x^{2}}{(x^{2}+25)^{\frac{3}{2}}}dx
derivative of 1/(-x^2)	\frac{d}{dx}(\frac{1}{-x^{2}})
(dy)/(dx)=x+2y,y(0)=6	\frac{dy}{dx}=x+2y,y(0)=6
limit as x approaches 0 of (pix^2+2)/x	\lim\:_{x\to\:0}(\frac{πx^{2}+2}{x})
(\partial)/(\partial x)(ln\|x\|)	\frac{\partial\:}{\partial\:x}(\ln\left\|x\right\|)
limit as x approaches 0 of 3xln(x)	\lim\:_{x\to\:0}(3x\ln(x))
limit as x approaches 3 of sqrt(8x^2+9)	\lim\:_{x\to\:3}(\sqrt{8x^{2}+9})
limit as x approaches a of \sqrt[3]{x}	\lim\:_{x\to\:a}(\sqrt[3]{x})
simplify (x-3)/(sqrt(x)-\sqrt{3)}	simplify\:\frac{x-3}{\sqrt{x}-\sqrt{3}}
area x^3,3x-2	area\:x^{3},3x-2
tangent of y=(27)/(x^2+9),(-3, 3/2)	tangent\:y=\frac{27}{x^{2}+9},(-3,\frac{3}{2})
limit as x approaches infinity+of 3x^2-8	\lim\:_{x\to\:\infty\:+}(3x^{2}-8)
derivative of f(x)=(1/4 x)^3	derivative\:f(x)=(\frac{1}{4}x)^{3}
derivative of (tan(x)^2)	\frac{d}{dx}((\tan(x))^{2})
y^'=-y-2x,y(0)=1	y^{\prime\:}=-y-2x,y(0)=1
(dy)/(dx)+4xy^3=0	\frac{dy}{dx}+4xy^{3}=0
derivative of f(x)=(-16x^2+36)^2	derivative\:f(x)=(-16x^{2}+36)^{2}
derivative of arctan(tanh(x))	\frac{d}{dx}(\arctan(\tanh(x)))
integral of (2x^3+1)/(x^2+x-6)	\int\:\frac{2x^{3}+1}{x^{2}+x-6}dx
integral of 1/(sqrt(2x^2-4x+6))	\int\:\frac{1}{\sqrt{2x^{2}-4x+6}}dx
integral from 0 to 1 of 2pix(33-33x)	\int\:_{0}^{1}2πx(33-33x)dx
limit as x approaches 0 of (4/(x+4)-1)/x	\lim\:_{x\to\:0}(\frac{\frac{4}{x+4}-1}{x})
integral from 0 to 1 of (73)/(x^5)	\int\:_{0}^{1}\frac{73}{x^{5}}dx
limit as x approaches-1 of (inx)/(x-1)	\lim\:_{x\to\:-1}(\frac{inx}{x-1})
(dy)/(dx)=2xy^2+72x	\frac{dy}{dx}=2xy^{2}+72x
tangent of f(x)=4x^2+3x	tangent\:f(x)=4x^{2}+3x
integral of x^3sqrt(x^2+25)	\int\:x^{3}\sqrt{x^{2}+25}dx
(dy)/(dx)= y/(y-x)	\frac{dy}{dx}=\frac{y}{y-x}
(\partial)/(\partial x)(2(xe^{x/2+y}+1))	\frac{\partial\:}{\partial\:x}(2(xe^{\frac{x}{2}+y}+1))
derivative of 2e^x+3x-ln(x)	\frac{d}{dx}(2e^{x}+3x-\ln(x))
integral of-1/2 sin(2x)	\int\:-\frac{1}{2}\sin(2x)dx
limit as x approaches 80 of 82-x	\lim\:_{x\to\:80}(82-x)
integral of 2sin(pix)	\int\:2\sin(πx)dx
derivative of x^4-6x^3	derivative\:x^{4}-6x^{3}
limit as x approaches-2-of 2x+1	\lim\:_{x\to\:-2-}(2x+1)
derivative of 2sin(8x)	\frac{d}{dx}(2\sin(8x))
slope of x-sqrt(x)	slope\:x-\sqrt{x}
y^'-y=2xe^{2x}	y^{\prime\:}-y=2xe^{2x}
f^'(x)=sqrt(x)(6+5x)	f^{\prime\:}(x)=\sqrt{x}(6+5x)
tangent of f(x)= 1/(sqrt(10x)),\at x=9	tangent\:f(x)=\frac{1}{\sqrt{10x}},\at\:x=9
integral of x^6+1/(sqrt(1-4x^2))	\int\:x^{6}+\frac{1}{\sqrt{1-4x^{2}}}dx
laplacetransform e^{-4t}	laplacetransform\:e^{-4t}
(i)^'	(i)^{\prime\:}
derivative of sqrt(1+tan^2(x))	\frac{d}{dx}(\sqrt{1+\tan^{2}(x)})
derivative of 1/((x^2+y^2))	\frac{d}{dx}(\frac{1}{(x^{2}+y^{2})})
(\partial)/(\partial x)(e^{7xy})	\frac{\partial\:}{\partial\:x}(e^{7xy})
integral of sin^3(x)-sin^5(x)	\int\:\sin^{3}(x)-\sin^{5}(x)dx
derivative of f(x)= x/(x^2-4)	derivative\:f(x)=\frac{x}{x^{2}-4}
9x^2y^'=y^'+6xe^{-y}	9x^{2}y^{\prime\:}=y^{\prime\:}+6xe^{-y}
y^'=y(xy^5+1)	y^{\prime\:}=y(xy^{5}+1)
area y=\|x\|,y=x^2-1	area\:y=\left\|x\right\|,y=x^{2}-1
taylor (cos(sqrt(x)))^{1/x}	taylor\:(\cos(\sqrt{x}))^{\frac{1}{x}}
area x=y^2-4y,x=0	area\:x=y^{2}-4y,x=0
y^'+(tan(t))y=tan(t)	y^{\prime\:}+(\tan(t))y=\tan(t)
derivative of y=(x^2+3x)^2	derivative\:y=(x^{2}+3x)^{2}
derivative of coth(x)	\frac{d}{dx}(\coth(x))
limit as x approaches 0+of e^{1/x}*x	\lim\:_{x\to\:0+}(e^{\frac{1}{x}}\cdot\:x)
limit as x approaches 1 of (x^4-1)/(x+1)	\lim\:_{x\to\:1}(\frac{x^{4}-1}{x+1})
limit as x approaches 4 of 5x+6	\lim\:_{x\to\:4}(5x+6)
limit as n approaches infinity of n/3	\lim\:_{n\to\:\infty\:}(\frac{n}{3})
derivative of (sin(1/x*x^3)/(ln(x)))	\frac{d}{dx}(\frac{\sin(\frac{1}{x})\cdot\:x^{3}}{\ln(x)})
implicit (dy)/(dx),(x-y)^2=2ax	implicit\:\frac{dy}{dx},(x-y)^{2}=2ax
derivative of (x^3/(x^2+2))	\frac{d}{dx}(\frac{x^{3}}{x^{2}+2})
derivative of 2x^3-6x^2	\frac{d}{dx}(2x^{3}-6x^{2})
y^'=y(1-0.0002y)	y^{\prime\:}=y(1-0.0002y)

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