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Popular Calculus Problems

derivative of f(x)=xsqrt(2x^2+7)	derivative\:f(x)=x\sqrt{2x^{2}+7}
derivative of (ln(x)-1)/(ln^2(x))	derivative\:\frac{\ln(x)-1}{\ln^{2}(x)}
integral of sin^2(5θ)	\int\:\sin^{2}(5θ)dθ
integral of (x^2-5x+3)/(x-7)	\int\:\frac{x^{2}-5x+3}{x-7}dx
x^2+y^2=xyy^'	x^{2}+y^{2}=xyy^{\prime\:}
inverse oflaplace e^{-2s}(1/(4s))	inverselaplace\:e^{-2s}(\frac{1}{4s})
integral of x(4-x^2)^{1/2}	\int\:x(4-x^{2})^{\frac{1}{2}}dx
(\partial)/(\partial y)(xye^{xy})	\frac{\partial\:}{\partial\:y}(xye^{xy})
integral of (x-sqrt(x))/3	\int\:\frac{x-\sqrt{x}}{3}dx
limit as x approaches 0 of ((x))/x	\lim\:_{x\to\:0}(\frac{(x)}{x})
integral of sqrt((3x+1)/(3x-1))	\int\:\sqrt{\frac{3x+1}{3x-1}}dx
limit as x approaches 1 of (\sqrt[3]{x+2}-1)/(x-1)	\lim\:_{x\to\:1}(\frac{\sqrt[3]{x+2}-1}{x-1})
derivative of x^2e^{-9x}	\frac{d}{dx}(x^{2}e^{-9x})
(\partial)/(\partial x)((100)/(x^2+y^2+3))	\frac{\partial\:}{\partial\:x}(\frac{100}{x^{2}+y^{2}+3})
integral of ((5+e^x)^2)/(e^x)	\int\:\frac{(5+e^{x})^{2}}{e^{x}}dx
sum from n=0 to infinity of (ln(n))/n	\sum\:_{n=0}^{\infty\:}\frac{\ln(n)}{n}
((16)/(x(4-x^2)))^'	(\frac{16}{x(4-x^{2})})^{\prime\:}
integral of tan^2(u)	\int\:\tan^{2}(u)du
integral of 4e^{-4x}sin(4x)	\int\:4e^{-4x}\sin(4x)dx
limit as x approaches 5 of (\|5-x\|)/(x-5)	\lim\:_{x\to\:5}(\frac{\left\|5-x\right\|}{x-5})
derivative of f(x)=4e^xcos(x)	derivative\:f(x)=4e^{x}\cos(x)
integral from 2 to 3 of tsin(pit)	\int\:_{2}^{3}t\sin(πt)dt
integral of ((x^5-x^3+2x))/(x^4)	\int\:\frac{(x^{5}-x^{3}+2x)}{x^{4}}dx
laplacetransform 1-e^{-t}	laplacetransform\:1-e^{-t}
integral of (6x^3+8x)/(x^4-16)	\int\:\frac{6x^{3}+8x}{x^{4}-16}dx
(dy)/(dx)=6x(y-1)^{2/3}	\frac{dy}{dx}=6x(y-1)^{\frac{2}{3}}
integral of (x^3-6x-20)/(x+5)	\int\:\frac{x^{3}-6x-20}{x+5}dx
derivative of tsin(pi)t	derivative\:t\sin(π)t
limit as x approaches 3 of sqrt(x^2-5)	\lim\:_{x\to\:3}(\sqrt{x^{2}-5})
y^'=((x+3y))/(2x)	y^{\prime\:}=\frac{(x+3y)}{2x}
derivative of f(x)=θcos(θ)	derivative\:f(x)=θ\cos(θ)
derivative of x^3-2	\frac{d}{dx}(x^{3}-2)
area f(x)=x^2+4,g(x)=-x^2-1,x=-2,x=3	area\:f(x)=x^{2}+4,g(x)=-x^{2}-1,x=-2,x=3
derivative of f(x)=(x^2-1)/(2x-3)	derivative\:f(x)=\frac{x^{2}-1}{2x-3}
(d^2y)/(dt^2)-4(dy)/(dt)-5y=0	\frac{d^{2}y}{dt^{2}}-4\frac{dy}{dt}-5y=0
derivative of (x^4+3x^2/((x^2+1)^2))	\frac{d}{dx}(\frac{x^{4}+3x^{2}}{(x^{2}+1)^{2}})
(\partial)/(\partial x)(A)	\frac{\partial\:}{\partial\:x}(A)
limit as x approaches 1 of (ln(x))/x	\lim\:_{x\to\:1}(\frac{\ln(x)}{x})
derivative of-2/x	derivative\:-\frac{2}{x}
integral of 1/(x^2(x+2))	\int\:\frac{1}{x^{2}(x+2)}dx
derivative of 3x^2+8x+2	derivative\:3x^{2}+8x+2
limit as x approaches 0 of (sqrt(2(x+h(x)))-sqrt(2x))/(h(x))	\lim\:_{x\to\:0}(\frac{\sqrt{2(x+h(x))}-\sqrt{2x}}{h(x)})
y^{''}+y=0,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}+y=0,y(0)=1,y^{\prime\:}(0)=1
laplacetransform 5t^3	laplacetransform\:5t^{3}
derivative of \sqrt[3]{1+x^2}	\frac{d}{dx}(\sqrt[3]{1+x^{2}})
f(t)=6cos(2t)	f(t)=6\cos(2t)
integral of 1/4 x^2-1/2 ln(x)	\int\:\frac{1}{4}x^{2}-\frac{1}{2}\ln(x)dx
integral of (sin^3(e^x))(cos(e^x))e^x	\int\:(\sin^{3}(e^{x}))(\cos(e^{x}))e^{x}dx
integral of x^2-3/x+cos(x)-2/(sqrt(x))	\int\:x^{2}-\frac{3}{x}+\cos(x)-\frac{2}{\sqrt{x}}dx
integral from-2 to 1 of x^{-4}	\int\:_{-2}^{1}x^{-4}dx
integral of 1/((1+5x)sqrt(5x))	\int\:\frac{1}{(1+5x)\sqrt{5x}}dx
derivative of 3/(x^2-4/(x^3))	\frac{d}{dx}(\frac{3}{x^{2}}-\frac{4}{x^{3}})
integral from 0 to 1 of (ln(x))/(5x)	\int\:_{0}^{1}\frac{\ln(x)}{5x}dx
y=2(x+y)(dy)/(dx)	y=2(x+y)\frac{dy}{dx}
derivative of x^{5/4}	derivative\:x^{\frac{5}{4}}
derivative of (sin(x+cos(x))^3)	\frac{d}{dx}((\sin(x)+\cos(x))^{3})
derivative of (1/2 x)^3	derivative\:(\frac{1}{2}x)^{3}
integral from 4 to 8 of x/(x^2+6x+13)	\int\:_{4}^{8}\frac{x}{x^{2}+6x+13}dx
derivative of 1/a sin(b+ax)	\frac{d}{dx}(\frac{1}{a}\sin(b+ax))
integral of e^{5x}cos(x)	\int\:e^{5x}\cos(x)dx
derivative of (8sqrt(x)+1/(x^{-5)})	\frac{d}{dx}(\frac{8\sqrt{x}+1}{x^{-5}})
integral of x^{n+2}	\int\:x^{n+2}dx
integral of (4x^2+9x+4)/((x^2+1)^2)	\int\:\frac{4x^{2}+9x+4}{(x^{2}+1)^{2}}dx
integral of ((1+x)^2)/(sqrt(x))	\int\:\frac{(1+x)^{2}}{\sqrt{x}}dx
integral of+1/(x^2+a^2)	\int\:+\frac{1}{x^{2}+a^{2}}dx
(dy)/(dx)=sqrt(4y)e^{x+4}	\frac{dy}{dx}=\sqrt{4y}e^{x+4}
(x+y)dy=(x-y)dx	(x+y)dy=(x-y)dx
tangent of f(x)=x^4-13x^2+36,\at x=-2	tangent\:f(x)=x^{4}-13x^{2}+36,\at\:x=-2
derivative of 5x^3-5x	\frac{d}{dx}(5x^{3}-5x)
(\partial)/(\partial x)(cos(0.6x-t))	\frac{\partial\:}{\partial\:x}(\cos(0.6x-t))
integral of (300)/(sqrt(2x+25))	\int\:\frac{300}{\sqrt{2x+25}}dx
(\partial)/(\partial x)(sin(y/x))	\frac{\partial\:}{\partial\:x}(\sin(\frac{y}{x}))
limit as x approaches-2 of 2x^3-x^2+7x-3	\lim\:_{x\to\:-2}(2x^{3}-x^{2}+7x-3)
slope of (2.6)(-2.6)	slope\:(2.6)(-2.6)
limit as x approaches 2 of (2/x-1)/(2-x)	\lim\:_{x\to\:2}(\frac{\frac{2}{x}-1}{2-x})
integral of (x^2-2x-1)/((x-1)^2(x^2+1))	\int\:\frac{x^{2}-2x-1}{(x-1)^{2}(x^{2}+1)}dx
integral of ((e^{2x}))/(sqrt(e^x+1))	\int\:\frac{(e^{2x})}{\sqrt{e^{x}+1}}dx
derivative of 7x^5	\frac{d}{dx}(7x^{5})
derivative of (x-3xsqrt(x))/(sqrt(x))	derivative\:\frac{x-3x\sqrt{x}}{\sqrt{x}}
derivative of (cos(x)/(-2sin(2x)))	\frac{d}{dx}(\frac{\cos(x)}{-2\sin(2x)})
(\partial)/(\partial r)(z)	\frac{\partial\:}{\partial\:r}(z)
derivative of 2/3 (x+3^{3/2})	\frac{d}{dx}(\frac{2}{3}(x+3)^{\frac{3}{2}})
13xdx=127(92)ydy	13xdx=127(92)ydy
x^'=1-x^2	x^{\prime\:}=1-x^{2}
integral of sqrt(3-4x^2)	\int\:\sqrt{3-4x^{2}}dx
integral of 12cos(x)	\int\:12\cos(x)dx
integral of (x^3-9x^2-1)/(x^2(x+1)(x-2))	\int\:\frac{x^{3}-9x^{2}-1}{x^{2}(x+1)(x-2)}dx
(\partial)/(\partial x)(e^{(xy)/(z^2)})	\frac{\partial\:}{\partial\:x}(e^{\frac{xy}{z^{2}}})
y^{''}=(2k)/(1-k)	y^{\prime\:\prime\:}=\frac{2k}{1-k}
derivative of x^2ln\|x\|	\frac{d}{dx}(x^{2}\ln\left\|x\right\|)
derivative of f(x)=(x^2+2x)/((x+1)^2)	derivative\:f(x)=\frac{x^{2}+2x}{(x+1)^{2}}
(\partial)/(\partial x)(4e^{yz}cos(xyz))	\frac{\partial\:}{\partial\:x}(4e^{yz}\cos(xyz))
limit as x approaches 7 of (-2)/(7-x)	\lim\:_{x\to\:7}(\frac{-2}{7-x})
tangent of y=(6x)/(x+2),(4,4)	tangent\:y=\frac{6x}{x+2},(4,4)
integral of ((x-2))/(x^2-7x+12)	\int\:\frac{(x-2)}{x^{2}-7x+12}dx
integral of 1/(xlog_{10)(x)}	\int\:\frac{1}{x\log_{10}(x)}dx
integral of (-18x^2-10)csc^2(3x^3+5x)	\int\:(-18x^{2}-10)\csc^{2}(3x^{3}+5x)dx
derivative of (2xsin(x)/(1+cos(x)))	\frac{d}{dx}(\frac{2x\sin(x)}{1+\cos(x)})
integral of 3x^2+e^y	\int\:3x^{2}+e^{y}dy
sum from n=3 to infinity of (4/11)^{-n}	\sum\:_{n=3}^{\infty\:}(\frac{4}{11})^{-n}

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