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Popular Calculus Problems

integral of (-sin(x))/(cos(x))	\int\:\frac{-\sin(x)}{\cos(x)}dx
integral of (2x)/(sqrt(x^2-4))	\int\:\frac{2x}{\sqrt{x^{2}-4}}dx
integral of 2e^{-2x}sin(2x)	\int\:2e^{-2x}\sin(2x)dx
(dy)/(dx)-2ytan(x)=y^2tan^2(x)	\frac{dy}{dx}-2y\tan(x)=y^{2}\tan^{2}(x)
derivative of f(x)=(x^2)/(e^x)	derivative\:f(x)=\frac{x^{2}}{e^{x}}
derivative of y= 2/(ln(x))	derivative\:y=\frac{2}{\ln(x)}
derivative of f(x)= 1/(x^7)	derivative\:f(x)=\frac{1}{x^{7}}
f(t)=2t^2	f(t)=2t^{2}
derivative of f(t)=(3t+1)^{2/3}	derivative\:f(t)=(3t+1)^{\frac{2}{3}}
derivative of 5^{sin(x})	\frac{d}{dx}(5^{\sin(x)})
derivative of x^2cos^2(x)	\frac{d}{dx}(x^{2}\cos^{2}(x))
(dy)/(dt)=2t	\frac{dy}{dt}=2t
derivative of (e^{2x}/(x-3))	\frac{d}{dx}(\frac{e^{2x}}{x-3})
(dy)/(dt)=e^{-3t},y(0)=10	\frac{dy}{dt}=e^{-3t},y(0)=10
derivative of (x-1)^2(2x+1)^4	derivative\:(x-1)^{2}(2x+1)^{4}
(\partial)/(\partial x)(e^{x^2-y^2})	\frac{\partial\:}{\partial\:x}(e^{x^{2}-y^{2}})
y^'+2x^2y=x^2	y^{\prime\:}+2x^{2}y=x^{2}
integral of (2-2x)/(1-sqrt(x))	\int\:\frac{2-2x}{1-\sqrt{x}}dx
(dy)/(dx)+y/x =2x^8y^2	\frac{dy}{dx}+\frac{y}{x}=2x^{8}y^{2}
(\partial)/(\partial x)(arctan(9x))	\frac{\partial\:}{\partial\:x}(\arctan(9x))
derivative of y=(4x^2+3)(2x-3)	derivative\:y=(4x^{2}+3)(2x-3)
integral of 18arctan(sqrt(x))	\int\:18\arctan(\sqrt{x})dx
(d^2)/(dx^2)((2x-3)/(3x+1))	\frac{d^{2}}{dx^{2}}(\frac{2x-3}{3x+1})
tangent of f(x)=x^4+2*e^x,\at x=0	tangent\:f(x)=x^{4}+2\cdot\:e^{x},\at\:x=0
integral of 5sin((npix)/4)	\int\:5\sin(\frac{nπx}{4})dx
integral of 7^nln(7)	\int\:7^{n}\ln(7)dn
limit as x approaches 3 of 6+x	\lim\:_{x\to\:3}(6+x)
limit as x approaches 0-of e^{-1/x}	\lim\:_{x\to\:0-}(e^{-\frac{1}{x}})
sum from n=0 to infinity of sin^2(n)	\sum\:_{n=0}^{\infty\:}\sin^{2}(n)
integral of 1/(x^2+4x)	\int\:\frac{1}{x^{2}+4x}dx
derivative of (\sqrt[3]{x})/(x-9)	derivative\:\frac{\sqrt[3]{x}}{x-9}
tangent of (x^3-4x)^{10}	tangent\:(x^{3}-4x)^{10}
integral of 1/(x^2+7x+12)	\int\:\frac{1}{x^{2}+7x+12}dx
integral of (sec(x)tan(x)-(sec(x))^2)	\int\:(\sec(x)\tan(x)-(\sec(x))^{2})dx
derivative of ([3x^2]/([x^2-4]))	\frac{d}{dx}(\frac{[3x^{2}]}{[x^{2}-4]})
derivative of f(x)=3x^{1/3}-5x^{4/3}	derivative\:f(x)=3x^{\frac{1}{3}}-5x^{\frac{4}{3}}
inverse oflaplace 1/(((s-1)^2+4))	inverselaplace\:\frac{1}{((s-1)^{2}+4)}
derivative of (1-x/(x^2+1))	\frac{d}{dx}(\frac{1-x}{x^{2}+1})
y^{''}-4y+4y=0	y^{\prime\:\prime\:}-4y+4y=0
y^'=x(2-y)	y^{\prime\:}=x(2-y)
limit as x approaches-infinity of-3e^x	\lim\:_{x\to\:-\infty\:}(-3e^{x})
derivative of \|x^4-4x^2\|	\frac{d}{dx}(\left\|x^{4}-4x^{2}\right\|)
integral of cos^2(2θ)	\int\:\cos^{2}(2θ)dθ
integral of (3x^2)/((x^3+3)^2)	\int\:\frac{3x^{2}}{(x^{3}+3)^{2}}dx
(\partial)/(\partial x)(2x^2+9y^2)	\frac{\partial\:}{\partial\:x}(2x^{2}+9y^{2})
integral of 2e^{3x+e^{3x}}	\int\:2e^{3x+e^{3x}}dx
d/(dt)(2e^tcos(t))	\frac{d}{dt}(2e^{t}\cos(t))
(dP)/(dt)+2tP=P+6t-3	\frac{dP}{dt}+2tP=P+6t-3
integral of (2x+5)/(sqrt(16-6x-x^2))	\int\:\frac{2x+5}{\sqrt{16-6x-x^{2}}}dx
integral of x^3sqrt(x^2+31)	\int\:x^{3}\sqrt{x^{2}+31}dx
limit as x approaches 0 of In(x)	\lim\:_{x\to\:0}(In(x))
integral from-2 to 3 of (x-6)-(x^2-12)	\int\:_{-2}^{3}(x-6)-(x^{2}-12)dx
limit as x approaches 1 of 8/(x^3-1)	\lim\:_{x\to\:1}(\frac{8}{x^{3}-1})
limit as x approaches 0 of 7x	\lim\:_{x\to\:0}(7x)
derivative of ln((x+a/(x-a)))	\frac{d}{dx}(\ln(\frac{x+a}{x-a}))
limit as x approaches 0 of (\|-2x\|)/(5x)	\lim\:_{x\to\:0}(\frac{\left\|-2x\right\|}{5x})
(\partial)/(\partial x)(34)	\frac{\partial\:}{\partial\:x}(34)
integral from 0 to 4 of pie^{-x/2}	\int\:_{0}^{4}πe^{-\frac{x}{2}}dx
limit as x approaches 0 of 2^{(x-1)}	\lim\:_{x\to\:0}(2^{(x-1)})
inverse oflaplace 4/(s+5)	inverselaplace\:\frac{4}{s+5}
derivative of-4e^xsin(x)	\frac{d}{dx}(-4e^{x}\sin(x))
integral of 1/(x^4sqrt(16-25x^2))	\int\:\frac{1}{x^{4}\sqrt{16-25x^{2}}}dx
derivative of (x^2-16/(x+4))	\frac{d}{dx}(\frac{x^{2}-16}{x+4})
derivative of (x^2+3)(x^2-3)x^2	derivative\:(x^{2}+3)(x^{2}-3)x^{2}
integral of sec^2(x)tan^2(x)	\int\:\sec^{2}(x)\tan^{2}(x)dx
(\partial)/(\partial x)(-1/(x-y))	\frac{\partial\:}{\partial\:x}(-\frac{1}{x-y})
(\partial)/(\partial x)(4x^3y^3+1)	\frac{\partial\:}{\partial\:x}(4x^{3}y^{3}+1)
derivative of 2(x-2-2sin(2)(2x+1))	\frac{d}{dx}(2(x-2)-2\sin(2)(2x+1))
integral of 1/3 e^{-3x}	\int\:\frac{1}{3}e^{-3x}dx
integral of 9sin(t)	\int\:9\sin(t)dt
integral of sin(θ)cos(2θ)	\int\:\sin(θ)\cos(2θ)dθ
integral from 0 to r of xarcsin((r-x)/r)	\int\:_{0}^{r}x\arcsin(\frac{r-x}{r})dx
derivative of 1/(sin(2x))	\frac{d}{dx}(\frac{1}{\sin(2x)})
inverse oflaplace (e^{-s}-e^{-2s})/(s(s+2)(s+1))	inverselaplace\:\frac{e^{-s}-e^{-2s}}{s(s+2)(s+1)}
integral from 1 to sqrt(2 of)x8^{x^2}	\int\:_{1}^{\sqrt{2}}x8^{x^{2}}dx
y^'=(y(x-y))/(x^2)	y^{\prime\:}=\frac{y(x-y)}{x^{2}}
(dy)/(dx)=2+3y	\frac{dy}{dx}=2+3y
limit as x approaches 0 of ln(x^2)(-2)	\lim\:_{x\to\:0}(\ln(x^{2})(-2))
(\partial)/(\partial x)(x^2+3xy^2+2y)	\frac{\partial\:}{\partial\:x}(x^{2}+3xy^{2}+2y)
y^{''}+4y=2cos(2t)	y^{\prime\:\prime\:}+4y=2\cos(2t)
integral from 1 to b of (2x)/(x^2+4)	\int\:_{1}^{b}\frac{2x}{x^{2}+4}dx
x^2y+y^'=-3x^2	x^{2}y+y^{\prime\:}=-3x^{2}
tangent of f(x)=sqrt(1+4x),\at x=2	tangent\:f(x)=\sqrt{1+4x},\at\:x=2
limit as x approaches c of x^3+4x^2-3	\lim\:_{x\to\:c}(x^{3}+4x^{2}-3)
integral from 0 to 1 of (3+2x^2)	\int\:_{0}^{1}(3+2x^{2})dx
derivative of (-x^2-7)/((x^2-7)^2)	derivative\:\frac{-x^{2}-7}{(x^{2}-7)^{2}}
integral of (3x^2)/((2x^3-4)^2)	\int\:\frac{3x^{2}}{(2x^{3}-4)^{2}}dx
inverse oflaplace (2s-1)/(s^2-6s+18)	inverselaplace\:\frac{2s-1}{s^{2}-6s+18}
d/(dt)(12t)	\frac{d}{dt}(12t)
integral from 0 to 1 of e^{-st}	\int\:_{0}^{1}e^{-st}dt
integral of (x^x)	\int\:(x^{x})dx
(dy)/(dx)=x^5(x-xy)	\frac{dy}{dx}=x^{5}(x-xy)
sum from n=0 to infinity of 1/(sqrt(9))	\sum\:_{n=0}^{\infty\:}\frac{1}{\sqrt{9}}
integral of (5sqrt(x))/(x-1)	\int\:\frac{5\sqrt{x}}{x-1}dx
slope of (0,0),(6,4)	slope\:(0,0),(6,4)
integral from 0 to pi/2 of x^2sin(2x)	\int\:_{0}^{\frac{π}{2}}x^{2}\sin(2x)dx
limit as x approaches 0 of ((sin(4x)))/(2x)	\lim\:_{x\to\:0}(\frac{(\sin(4x))}{2x})
integral of 2sin^3(x)cos^5(x)	\int\:2\sin^{3}(x)\cos^{5}(x)dx
derivative of f(x)=arctan(3x)	derivative\:f(x)=\arctan(3x)
inverse oflaplace (s+1)/(s^2+4)	inverselaplace\:\frac{s+1}{s^{2}+4}

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