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Popular Calculus Problems

inverse oflaplace (3s+4)/((s^2+4s+5))	inverselaplace\:\frac{3s+4}{(s^{2}+4s+5)}
(\partial)/(\partial x)(x/(x^5-y^6))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{5}-y^{6}})
integral of (cos^2(x))/(sin(x))	\int\:\frac{\cos^{2}(x)}{\sin(x)}dx
(\partial)/(\partial x)(((x+y))/((x-y)))	\frac{\partial\:}{\partial\:x}(\frac{(x+y)}{(x-y)})
laplacetransform e^t*cos(t)	laplacetransform\:e^{t}\cdot\:\cos(t)
derivative of 2/3 sin((x+1/(x-1)))	\frac{d}{dx}(\frac{2}{3}\sin(\frac{x+1}{x-1}))
y^{''}+4y^'-21y=0	y^{\prime\:\prime\:}+4y^{\prime\:}-21y=0
integral of csc(t)cot(t)	\int\:\csc(t)\cot(t)dt
integral of sin^4(x)	\int\:\sin^{4}(x)dx
parity arcsin(sqrt(sin(11θ)))	parity\:\arcsin(\sqrt{\sin(11θ)})
derivative of (1/(x^2)-3/(x^4))(x+7x^3)	derivative\:(\frac{1}{x^{2}}-\frac{3}{x^{4}})(x+7x^{3})
(5y-2x)((dy)/(dx))-2y=0	(5y-2x)(\frac{dy}{dx})-2y=0
integral of 1/(sqrt(-t^2+6t-5))	\int\:\frac{1}{\sqrt{-t^{2}+6t-5}}dt
integral of 10x^5-10x^2+7	\int\:10x^{5}-10x^{2}+7dx
(dy)/(dx)= x/(25y)	\frac{dy}{dx}=\frac{x}{25y}
integral from 0 to 1 of 1+x^3	\int\:_{0}^{1}1+x^{3}dx
limit as x approaches 1 of e^x(x^3-4)	\lim\:_{x\to\:1}(e^{x}(x^{3}-4))
slope ofintercept (5)(0.5)	slopeintercept\:(5)(0.5)
f(x)=5sec(x)	f(x)=5\sec(x)
integral of tan(x)+4^x	\int\:\tan(x)+4^{x}dx
derivative of (1-x/2 ^{e^{x^2}})	\frac{d}{dx}((1-\frac{x}{2})^{e^{x^{2}}})
area y=x^2-7,y=2	area\:y=x^{2}-7,y=2
limit as x approaches 2 of-x^3+2x^2-1	\lim\:_{x\to\:2}(-x^{3}+2x^{2}-1)
derivative of arctan(sqrt(1+x^2))	\frac{d}{dx}(\arctan(\sqrt{1+x^{2}}))
((100)/(ln(2x+1)))^'	(\frac{100}{\ln(2x+1)})^{\prime\:}
integral of 2y^2ln(y)	\int\:2y^{2}\ln(y)dy
derivative of 7e^{x^2}	derivative\:7e^{x^{2}}
integral of (tan^2(x))/(sin(x))	\int\:\frac{\tan^{2}(x)}{\sin(x)}dx
integral of x^2-2y	\int\:x^{2}-2ydy
(dy)/(dx)=2xsqrt(1-y^2)	\frac{dy}{dx}=2x\sqrt{1-y^{2}}
dy-(y-1)2dx=0	dy-(y-1)2dx=0
limit as x approaches 5 of (\|5-x\|)/(5-x)	\lim\:_{x\to\:5}(\frac{\left\|5-x\right\|}{5-x})
(\partial)/(\partial x)(e^{x+6y})	\frac{\partial\:}{\partial\:x}(e^{x+6y})
derivative of ln(x^2+2x)(x^4+3x^2)^5	derivative\:\ln(x^{2}+2x)(x^{4}+3x^{2})^{5}
derivative of 12-3x^2	\frac{d}{dx}(12-3x^{2})
limit as x approaches 0 of (tan(x^2))/x	\lim\:_{x\to\:0}(\frac{\tan(x^{2})}{x})
derivative of (cos(2x)^2)	\frac{d}{dx}((\cos(2x))^{2})
area 4/x ,16x, 1/4 x	area\:\frac{4}{x},16x,\frac{1}{4}x
integral of (x^2)/((144+x^2)^2)	\int\:\frac{x^{2}}{(144+x^{2})^{2}}dx
limit as x approaches a of 1/(-6-4)	\lim\:_{x\to\:a}(\frac{1}{-6-4})
integral of 18cos^2(t)sin(t)	\int\:18\cos^{2}(t)\sin(t)dt
derivative of arccsc(2x+1)	\frac{d}{dx}(\arccsc(2x+1))
derivative of 3-(18/(5x^{1/10)})	\frac{d}{dx}(3-\frac{18}{5x^{\frac{1}{10}}})
limit as x approaches 0 of arctan(5/x)	\lim\:_{x\to\:0}(\arctan(\frac{5}{x}))
integral of 6cos(x)	\int\:6\cos(x)dx
derivative of f(x)=sqrt(8-x)	derivative\:f(x)=\sqrt{8-x}
xy^'-y=2x^2y	xy^{\prime\:}-y=2x^{2}y
y^{''}+18y^'+81y=t^{-2}e^{-9t}	y^{\prime\:\prime\:}+18y^{\prime\:}+81y=t^{-2}e^{-9t}
limit as x approaches-5 of (x^2-2)/(x+5)	\lim\:_{x\to\:-5}(\frac{x^{2}-2}{x+5})
integral of 1/((x+1)(x^2+4))	\int\:\frac{1}{(x+1)(x^{2}+4)}dx
-6y^{''}+54y^'=0,y(2)=1,y^'(-1)=1	-6y^{\prime\:\prime\:}+54y^{\prime\:}=0,y(2)=1,y^{\prime\:}(-1)=1
integral from 1 to 2 of 2x(1-1/(x^2))	\int\:_{1}^{2}2x(1-\frac{1}{x^{2}})dx
derivative of 5\sqrt[3]{x}+x^3	\frac{d}{dx}(5\sqrt[3]{x}+x^{3})
derivative of f(x)=(3t-1)^4(2t+1)^{-3}	derivative\:f(x)=(3t-1)^{4}(2t+1)^{-3}
integral of 1/((4-x)^{3/2)}	\int\:\frac{1}{(4-x)^{\frac{3}{2}}}dx
derivative of f(x)=e^{\sqrt[3]{5x}}	derivative\:f(x)=e^{\sqrt[3]{5x}}
sum from n=1 to infinity of (5n)/(4n+7)	\sum\:_{n=1}^{\infty\:}\frac{5n}{4n+7}
inverse oflaplace 8/((s^2+1)(s^2-1))	inverselaplace\:\frac{8}{(s^{2}+1)(s^{2}-1)}
integral of (sqrt(a^2-x^2))/(x^4)	\int\:\frac{\sqrt{a^{2}-x^{2}}}{x^{4}}dx
limit as x approaches 2 of x+3	\lim\:_{x\to\:2}(x+3)
derivative of y=ln(log_{e}(2x))	derivative\:y=\ln(\log_{e}(2x))
sum from n=1 to infinity of (x-2)^n	\sum\:_{n=1}^{\infty\:}(x-2)^{n}
integral of cos(x)sqrt(1+sin^2(x))	\int\:\cos(x)\sqrt{1+\sin^{2}(x)}dx
derivative of (4x^3/3-x)	\frac{d}{dx}(\frac{4x^{3}}{3}-x)
derivative of y=(x-2)(x+1)(x+2)	derivative\:y=(x-2)(x+1)(x+2)
integral of a^{-3x}	\int\:a^{-3x}dx
integral of (e^{3x})/((4+e^{2x))^2}	\int\:\frac{e^{3x}}{(4+e^{2x})^{2}}dx
tangent of f(x)= 8/(sqrt(x+11)),\at x=5	tangent\:f(x)=\frac{8}{\sqrt{x+11}},\at\:x=5
integral from 0 to 1 of 3x	\int\:_{0}^{1}3xdx
xy^'=x-y	xy^{\prime\:}=x-y
area (x-1)^2,x+1	area\:(x-1)^{2},x+1
derivative of y=(t+3)in(t)	derivative\:y=(t+3)in(t)
derivative of (x^2-4x+2/(x+3))	\frac{d}{dx}(\frac{x^{2}-4x+2}{x+3})
integral of 1-1	\int\:1-1dx
integral of sqrt(1/(4+x^2))	\int\:\sqrt{\frac{1}{4+x^{2}}}dx
integral of x^3sqrt(x+10)	\int\:x^{3}\sqrt{x+10}dx
limit as x approaches 0 of tan(x^2)	\lim\:_{x\to\:0}(\tan(x^{2}))
(dy)/(dx)= 2/(sqrt(16-x^2))	\frac{dy}{dx}=\frac{2}{\sqrt{16-x^{2}}}
integral of (e^{1-x})	\int\:(e^{1-x})dx
derivative of 1/10 x-1/8	\frac{d}{dx}(\frac{1}{10}x-\frac{1}{8})
sum from n=0 to infinity of 1/(n^{-1)}	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{-1}}
integral of (x^{-1/3})	\int\:(x^{-\frac{1}{3}})dx
integral of sin(bx)	\int\:\sin(bx)dx
inverse oflaplace 1/((s-3)^2)	inverselaplace\:\frac{1}{(s-3)^{2}}
integral of (2cos(x))/(5+sin^2(x))	\int\:\frac{2\cos(x)}{5+\sin^{2}(x)}dx
integral of 70xe^{7x^2}	\int\:70xe^{7x^{2}}dx
limit as x approaches 0 of (sqrt(2-x))/x	\lim\:_{x\to\:0}(\frac{\sqrt{2-x}}{x})
derivative of sec(3x)	derivative\:\sec(3x)
derivative of (x^2+1)/(x+4)	derivative\:\frac{x^{2}+1}{x+4}
inverse oflaplace 1/(6s)	inverselaplace\:\frac{1}{6s}
integral of 1/(θ^2)cos(1/θ)	\int\:\frac{1}{θ^{2}}\cos(\frac{1}{θ})dθ
(\partial)/(\partial x)(e^{sin(2x)})	\frac{\partial\:}{\partial\:x}(e^{\sin(2x)})
derivative of e^{tanh(x})	\frac{d}{dx}(e^{\tanh(x)})
derivative of 1+sqrt(x)	derivative\:1+\sqrt{x}
(dy)/(dx)=-(5y)/(50+x)	\frac{dy}{dx}=-\frac{5y}{50+x}
derivative of y=e^{7e^x}	derivative\:y=e^{7e^{x}}
integral of 24t^2+16t	\int\:24t^{2}+16tdt
tangent of f(x)=sqrt(x^2+24),\at x=5	tangent\:f(x)=\sqrt{x^{2}+24},\at\:x=5
xy^'=5y-x,y(1)=1	xy^{\prime\:}=5y-x,y(1)=1
integral of (arccos(sqrt(x)))/(sqrt(x))	\int\:\frac{\arccos(\sqrt{x})}{\sqrt{x}}dx

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