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Popular Calculus Problems

area x=4y,x=y^2-5	area\:x=4y,x=y^{2}-5
integral from-4 to 4 of (2x^7+1)	\int\:_{-4}^{4}(2x^{7}+1)dx
derivative of (1/(y^2)-9/(y^4))(y+3y^3)	derivative\:(\frac{1}{y^{2}}-\frac{9}{y^{4}})(y+3y^{3})
integral from 2 to 4 of f(x)	\int\:_{2}^{4}f(x)dx
f^'(x)= 4/x	f^{\prime\:}(x)=\frac{4}{x}
integral of 1/(sqrt(36x^2+2))	\int\:\frac{1}{\sqrt{36x^{2}+2}}dx
integral from 0 to 1/2 of cos^3(pix)	\int\:_{0}^{\frac{1}{2}}\cos^{3}(πx)dx
derivative of (x^4+9x^2-7^8)	\frac{d}{dx}((x^{4}+9x^{2}-7)^{8})
derivative of ln((7x^{ln(2x)}))	\frac{d}{dx}(\ln((7x)^{\ln(2x)}))
(\partial)/(\partial z)(8ze^{xyz})	\frac{\partial\:}{\partial\:z}(8ze^{xyz})
d/(dt)(ccos(t)+t^2sin(t))	\frac{d}{dt}(c\cos(t)+t^{2}\sin(t))
integral of 6/(x^2(x^2+25))	\int\:\frac{6}{x^{2}(x^{2}+25)}dx
limit as x approaches 0 of x^2+x+1	\lim\:_{x\to\:0}(x^{2}+x+1)
e^{x-y}y^'=x-3	e^{x-y}y^{\prime\:}=x-3
(\partial)/(\partial z)(x^2+y^2z)	\frac{\partial\:}{\partial\:z}(x^{2}+y^{2}z)
laplacetransform-8e^{pi-t}	laplacetransform\:-8e^{π-t}
derivative of (x^3+2x^2)^{-1}	derivative\:(x^{3}+2x^{2})^{-1}
sum from n=1 to infinity of arctan(n+1)	\sum\:_{n=1}^{\infty\:}\arctan(n+1)
limit as z approaches i of z(z+1)	\lim\:_{z\to\:i}(z(z+1))
derivative of 1/(ln^2(x))	\frac{d}{dx}(\frac{1}{\ln^{2}(x)})
integral of 1/(xsqrt(9x^2+16))	\int\:\frac{1}{x\sqrt{9x^{2}+16}}dx
integral of t^2sqrt(t^3+1)	\int\:t^{2}\sqrt{t^{3}+1}dt
integral of (r^3)/(sqrt(4+r^2))	\int\:\frac{r^{3}}{\sqrt{4+r^{2}}}dr
limit as x approaches 2-of (1-x)/(x-2)	\lim\:_{x\to\:2-}(\frac{1-x}{x-2})
xy^'-2y=12x^2	xy^{\prime\:}-2y=12x^{2}
derivative of x^2+5x-8	\frac{d}{dx}(x^{2}+5x-8)
-18y^{''}-14y^'=0,y(3)=-3,y^'(3)=-3	-18y^{\prime\:\prime\:}-14y^{\prime\:}=0,y(3)=-3,y^{\prime\:}(3)=-3
integral of (3x)/(sqrt(x^2-11))	\int\:\frac{3x}{\sqrt{x^{2}-11}}dx
integral of (4xe^x+e^{4x})/(e^{3x)}	\int\:\frac{4xe^{x}+e^{4x}}{e^{3x}}dx
integral from 1 to 4 of f(x)	\int\:_{1}^{4}f(x)dx
derivative of x(x^5+1^3)	\frac{d}{dx}(x(x^{5}+1)^{3})
(\partial)/(\partial y)(xe^y-ln(x))	\frac{\partial\:}{\partial\:y}(xe^{y}-\ln(x))
derivative of-x-1/x	derivative\:-x-\frac{1}{x}
limit as x approaches 0 of x^{-1}	\lim\:_{x\to\:0}(x^{-1})
integral from-2 to 3 of (14)/(x^4)	\int\:_{-2}^{3}\frac{14}{x^{4}}dx
derivative of xe^xsin(y)	\frac{d}{dx}(xe^{x}\sin(y))
y^{''}+3y^'-7y=x^4e^x	y^{\prime\:\prime\:}+3y^{\prime\:}-7y=x^{4}e^{x}
area y=x^2-2x+2,y=4	area\:y=x^{2}-2x+2,y=4
limit as x approaches 0 of xcot(1/4 x)	\lim\:_{x\to\:0}(x\cot(\frac{1}{4}x))
x^{''}+2x^'+5x=0	x^{\prime\:\prime\:}+2x^{\prime\:}+5x=0
derivative of (e^x+e^{-x})/(e^x-e^{-x)}	derivative\:\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}
integral of y/(sqrt(16-9y^4))	\int\:\frac{y}{\sqrt{16-9y^{4}}}dy
integral of (2x^3+x)(x^4+x^2)	\int\:(2x^{3}+x)(x^{4}+x^{2})dx
derivative of f(x)=-2x+7	derivative\:f(x)=-2x+7
integral of 7x^9-3x^6+10x^3	\int\:7x^{9}-3x^{6}+10x^{3}dx
limit as x approaches 0 of (e^{bx}-1)/x	\lim\:_{x\to\:0}(\frac{e^{bx}-1}{x})
limit as x approaches+1 of x/((x-1))	\lim\:_{x\to\:+1}(\frac{x}{(x-1)})
limit as x approaches 0 of (x-6)/(x-2)	\lim\:_{x\to\:0}(\frac{x-6}{x-2})
(d^3)/(dx^3)(sqrt(1+x))	\frac{d^{3}}{dx^{3}}(\sqrt{1+x})
(dy)/(dx)=12	\frac{dy}{dx}=12
derivative of x+1/(x+2)	\frac{d}{dx}(x+\frac{1}{x+2})
derivative of f(x)=sqrt(x)(x+3)	derivative\:f(x)=\sqrt{x}(x+3)
derivative of sqrt(6-3x)	\frac{d}{dx}(\sqrt{6-3x})
y^'=3y+7,y(0)=4	y^{\prime\:}=3y+7,y(0)=4
laplacetransform t^2+2	laplacetransform\:t^{2}+2
integral of 7xe^{4x}	\int\:7xe^{4x}dx
xyy^'+y^2=2x	xyy^{\prime\:}+y^{2}=2x
integral of 3x^3+3x-3	\int\:3x^{3}+3x-3dx
integral from 0 to 8 of xsqrt(64-x^2)	\int\:_{0}^{8}x\sqrt{64-x^{2}}dx
integral of sin(pi)tcos(pi)t	\int\:\sin(π)t\cos(π)tdt
derivative of (4x^2-5x+1)/x	derivative\:\frac{4x^{2}-5x+1}{x}
derivative of (x^2/(x^3+1))	\frac{d}{dx}(\frac{x^{2}}{x^{3}+1})
derivative of 4/(x^7-e^{-8x})	\frac{d}{dx}(\frac{4}{x^{7}}-e^{-8x})
integral of x/((x+1)(x+2))	\int\:\frac{x}{(x+1)(x+2)}dx
(\partial)/(\partial x)(1.015sqrt(E(m,x)bh^3m^{-1)L^{-4}})	\frac{\partial\:}{\partial\:x}(1.015\sqrt{E(m,x)bh^{3}m^{-1}L^{-4}})
derivative of cot^4(x-csc^4(x))	\frac{d}{dx}(\cot^{4}(x)-\csc^{4}(x))
derivative of y=2^{2x}	derivative\:y=2^{2x}
derivative of y=e^{in(x^2+1)}	derivative\:y=e^{in(x^{2}+1)}
limit as x approaches 2 of (\sqrt[3]{3x^2-2x-8})/((x+2)^3)	\lim\:_{x\to\:2}(\frac{\sqrt[3]{3x^{2}-2x-8}}{(x+2)^{3}})
taylor 1/((1+x^2))	taylor\:\frac{1}{(1+x^{2})}
integral of (x^2)/(sqrt(9-x^2))	\int\:\frac{x^{2}}{\sqrt{9-x^{2}}}dx
derivative of ln(sqrt(sin(3^{x^2)}))	\frac{d}{dx}(\ln(\sqrt{\sin(3^{x^{2}})}))
(x^2+y^2)dx-2xydy=0	(x^{2}+y^{2})dx-2xydy=0
derivative of 1-ln(3x)	derivative\:1-\ln(3x)
tangent of f(x)=3x^2,\at x=1	tangent\:f(x)=3x^{2},\at\:x=1
derivative of x(4x+1^{1/3})	\frac{d}{dx}(x(4x+1)^{\frac{1}{3}})
integral of t/(t-2)	\int\:\frac{t}{t-2}dt
integral of 1/(x-c)	\int\:\frac{1}{x-c}dx
integral of (x^4-2x^2+1)/(x^3)	\int\:\frac{x^{4}-2x^{2}+1}{x^{3}}dx
limit as x approaches 1-of 4x-5	\lim\:_{x\to\:1-}(4x-5)
derivative of 2/(3x)	derivative\:\frac{2}{3x}
integral of-(12)/(x^{13)}	\int\:-\frac{12}{x^{13}}dx
tangent of y=sqrt(x+3),(6,3)	tangent\:y=\sqrt{x+3},(6,3)
(dy)/(dx)=2e^{x-y}	\frac{dy}{dx}=2e^{x-y}
integral of (x^3)/(x^4-x^2+2)	\int\:\frac{x^{3}}{x^{4}-x^{2}+2}dx
derivative of f(x)=(3x+7)e^x	derivative\:f(x)=(3x+7)e^{x}
derivative of sqrt(x^2+10)	derivative\:\sqrt{x^{2}+10}
derivative of 1.394(1.006^x)	\frac{d}{dx}(1.394(1.006)^{x})
integral of 1/((x^2-196)^{3/2)}	\int\:\frac{1}{(x^{2}-196)^{\frac{3}{2}}}dx
derivative of arccot(sqrt(4x))	\frac{d}{dx}(\arccot(\sqrt{4x}))
derivative of y^2(2-x-x^3)	\frac{d}{dx}(y^{2}(2-x)-x^{3})
derivative of x^2+2	derivative\:x^{2}+2
y^'+3y=0,y(0)=0	y^{\prime\:}+3y=0,y(0)=0
(\partial)/(\partial x)(e^{(y+1)x})	\frac{\partial\:}{\partial\:x}(e^{(y+1)x})
derivative of f(x)=(x^3+9x^2+x-8)/x	derivative\:f(x)=\frac{x^{3}+9x^{2}+x-8}{x}
(\partial)/(\partial x)(sqrt(4ax))	\frac{\partial\:}{\partial\:x}(\sqrt{4ax})
derivative of (x^2+6^9)	\frac{d}{dx}((x^{2}+6)^{9})
derivative of cosh(4x)	\frac{d}{dx}(\cosh(4x))
(\partial)/(\partial y)(e^{2x+3y})	\frac{\partial\:}{\partial\:y}(e^{2x+3y})
limit as x approaches 1+of x+2	\lim\:_{x\to\:1+}(x+2)

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