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Popular Calculus Problems

limit as x approaches pi of 1	\lim\:_{x\to\:π}(1)
integral of tan(x)+cot(x)	\int\:\tan(x)+\cot(x)dx
derivative of f(x)=(e^{5x})/(2x-5)	derivative\:f(x)=\frac{e^{5x}}{2x-5}
integral from 0 to ln(3) of 2e^{3x}	\int\:_{0}^{\ln(3)}2e^{3x}dx
integral of (x^3+ex)sqrt(x^2+e)	\int\:(x^{3}+ex)\sqrt{x^{2}+e}dx
derivative of-4xsin(2x^2)	derivative\:-4x\sin(2x^{2})
tangent of f(x)=-8(4x+3)^{-3},\at x=3	tangent\:f(x)=-8(4x+3)^{-3},\at\:x=3
derivative of \sqrt[3]{x}-7/(x^3+e^2)	\frac{d}{dx}(\sqrt[3]{x}-\frac{7}{x^{3}}+e^{2})
derivative of cot(x+csc(x))	\frac{d}{dx}(\cot(x)+\csc(x))
limit as x approaches 1 of (1-x^2)/(ln(x))	\lim\:_{x\to\:1}(\frac{1-x^{2}}{\ln(x)})
y^'+(4y)/x =-3/x	y^{\prime\:}+\frac{4y}{x}=-\frac{3}{x}
derivative of 2e^{-1.5x}cos(3x)	\frac{d}{dx}(2e^{-1.5x}\cos(3x))
integral of (2x)/(sqrt(1+x^2))	\int\:\frac{2x}{\sqrt{1+x^{2}}}dx
slope of (2,5),(8,12)	slope\:(2,5),(8,12)
integral of e^{2x+y}	\int\:e^{2x+y}dx
integral of (sqrt(4-9x^2))/x	\int\:\frac{\sqrt{4-9x^{2}}}{x}dx
limit as x approaches 0-of (x^2)/2-8/x	\lim\:_{x\to\:0-}(\frac{x^{2}}{2}-\frac{8}{x})
limit as x approaches 2 of \|x-2\|	\lim\:_{x\to\:2}(\left\|x-2\right\|)
limit as x approaches 0-of (e^x)/x	\lim\:_{x\to\:0-}(\frac{e^{x}}{x})
limit as x approaches 1 of ln(7x)+e^x	\lim\:_{x\to\:1}(\ln(7x)+e^{x})
derivative of f(x)=20sqrt(x)	derivative\:f(x)=20\sqrt{x}
derivative of y=(x^2)/(e^x)	derivative\:y=\frac{x^{2}}{e^{x}}
derivative of x^{\sqrt[3]{x}}	\frac{d}{dx}(x^{\sqrt[3]{x}})
integral of (5x-2)/(x^2-4)	\int\:\frac{5x-2}{x^{2}-4}dx
derivative of sin(8x+4)	\frac{d}{dx}(\sin(8x+4))
derivative of (f(x(4x))^2+2)	\frac{d}{dx}((f(x)(4x))^{2}+2)
derivative of cos(at)	\frac{d}{dx}(\cos(at))
derivative of 9/(x^2)	derivative\:\frac{9}{x^{2}}
tangent of-0.025x^2+8x	tangent\:-0.025x^{2}+8x
y^'=xy^2+2y^2,y(0)=1	y^{\prime\:}=xy^{2}+2y^{2},y(0)=1
derivative of f(x)=(2x^2-6x+5)/(2(2x-3))	derivative\:f(x)=\frac{2x^{2}-6x+5}{2(2x-3)}
(dy)/(dx)=4xe^{3y}	\frac{dy}{dx}=4xe^{3y}
xy^'+2y=4cos(x)	xy^{\prime\:}+2y=4\cos(x)
(dy)/(dx)=sec^2(x)(2+y)^2	\frac{dy}{dx}=\sec^{2}(x)(2+y)^{2}
inverse oflaplace (4e^{-2s})/(3s^2+48)	inverselaplace\:\frac{4e^{-2s}}{3s^{2}+48}
(2y^2x-3)dx+(2yx^2+4)dy=0	(2y^{2}x-3)dx+(2yx^{2}+4)dy=0
inverse oflaplace (s+6)/(s^2+6s+25)	inverselaplace\:\frac{s+6}{s^{2}+6s+25}
integral of (sqrt(t-3))/(sqrt(t+1))	\int\:\frac{\sqrt{t-3}}{\sqrt{t+1}}dt
area y=x^3-2x^2+2,y=3x^2+5x-23	area\:y=x^{3}-2x^{2}+2,y=3x^{2}+5x-23
((x^2+1)dy)/(dx)+6x(y-1)=0,y(0)=3	\frac{(x^{2}+1)dy}{dx}+6x(y-1)=0,y(0)=3
t(dy)/(dt)=(t^3+22t^3*y)	t\frac{dy}{dt}=(t^{3}+22t^{3}\cdot\:y)
integral of (x^8)/(1+x^{18)}	\int\:\frac{x^{8}}{1+x^{18}}dx
derivative of 2xe^{x^2-1}	\frac{d}{dx}(2xe^{x^{2}-1})
tangent of f(30)=(850)/d	tangent\:f(30)=\frac{850}{d}
derivative of 5/(x+7)	\frac{d}{dx}(\frac{5}{x+7})
limit as x approaches-2 of (x+1)/(x^2-2)	\lim\:_{x\to\:-2}(\frac{x+1}{x^{2}-2})
(dy)/(dx)=(cos(18x))/(e^{18y)}	\frac{dy}{dx}=\frac{\cos(18x)}{e^{18y}}
integral of (1-y)/(y^2)	\int\:\frac{1-y}{y^{2}}dy
derivative of f(θ)=θsin(θ)	derivative\:f(θ)=θ\sin(θ)
inverse oflaplace (s+5)/((s+10)^2)	inverselaplace\:\frac{s+5}{(s+10)^{2}}
(d^5)/(dx^5)(sqrt(x))	\frac{d^{5}}{dx^{5}}(\sqrt{x})
derivative of ((x^2+1)/(2x^2-3x))	\frac{d}{dx}(\frac{(x^{2}+1)}{2x^{2}-3x})
derivative of f(x)=(9x^6+8x^3)^4	derivative\:f(x)=(9x^{6}+8x^{3})^{4}
integral of 5x^2sqrt(x+9)	\int\:5x^{2}\sqrt{x+9}dx
derivative of f(x)=9x+4x^{-1}	derivative\:f(x)=9x+4x^{-1}
integral from 0 to 1 of (y^6+y^8)	\int\:_{0}^{1}(y^{6}+y^{8})dy
derivative of f(x)=(\sqrt[3]{t})/(t-3)	derivative\:f(x)=\frac{\sqrt[3]{t}}{t-3}
limit as x approaches 1+of 1/x-1	\lim\:_{x\to\:1+}(\frac{1}{x}-1)
area y=4x,y=6x^2	area\:y=4x,y=6x^{2}
integral of 3x^2sqrt(a^2-x^2)	\int\:3x^{2}\sqrt{a^{2}-x^{2}}dx
y^{''}+2y^'+4y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+4y=0,y(0)=1,y^{\prime\:}(0)=0
integral from 0 to 2 of 1/(x+1)	\int\:_{0}^{2}\frac{1}{x+1}dx
integral of (x^2-2x+1)^3	\int\:(x^{2}-2x+1)^{3}dx
integral of tsin(t)	\int\:t\sin(t)dt
laplacetransform 7sin(4(t+2))+3cos(4t-2)	laplacetransform\:7\sin(4(t+2))+3\cos(4t-2)
derivative of ln((5x+3/(5x-3)))	\frac{d}{dx}(\ln(\frac{5x+3}{5x-3}))
integral of 2cot(2x)	\int\:2\cot(2x)dx
integral from 0 to 4pi of sqrt(5+t^2)	\int\:_{0}^{4π}\sqrt{5+t^{2}}dt
integral of (x^2)/((6-x^3)^2)	\int\:\frac{x^{2}}{(6-x^{3})^{2}}dx
sum from n=0 to infinity of 3/((n+1))	\sum\:_{n=0}^{\infty\:}\frac{3}{(n+1)}
derivative of (x^3)/2+1/(6x)	derivative\:\frac{x^{3}}{2}+\frac{1}{6x}
derivative of 3cos(sqrt(x)sin(x))	\frac{d}{dx}(3\cos(\sqrt{x}\sin(x)))
sum from n=1 to infinity of n/(n^2+9)	\sum\:_{n=1}^{\infty\:}\frac{n}{n^{2}+9}
tangent of f(x)=2x^2-5x,\at x=3	tangent\:f(x)=2x^{2}-5x,\at\:x=3
integral from 0 to 3 of 9x-x^3	\int\:_{0}^{3}9x-x^{3}dx
integral of (tan(x))^3	\int\:(\tan(x))^{3}dx
integral of 5sin^2(xco)s^3x	\int\:5\sin^{2}(xco)s^{3}xdx
limit as x approaches 5-of (x-5)/(\|x-5\|)	\lim\:_{x\to\:5-}(\frac{x-5}{\left\|x-5\right\|})
integral of sinh(sqrt(x))	\int\:\sinh(\sqrt{x})dx
derivative of ((x^2/(x^3-4x))^3)	\frac{d}{dx}((\frac{x^{2}}{x^{3}-4x})^{3})
derivative of (x^n/(n!))	\frac{d}{dx}(\frac{x^{n}}{n!})
integral from 0 to pi of sin^4(2x)	\int\:_{0}^{π}\sin^{4}(2x)dx
limit as x approaches-infinity of x*e^x	\lim\:_{x\to\:-\infty\:}(x\cdot\:e^{x})
d/(dy)(sin^2(y))	\frac{d}{dy}(\sin^{2}(y))
integral from-10 to 10 of pi(100-x^2)	\int\:_{-10}^{10}π(100-x^{2})dx
(\partial)/(\partial y)((-2y)/((2x+3y)^2))	\frac{\partial\:}{\partial\:y}(\frac{-2y}{(2x+3y)^{2}})
derivative of-3/((1+3x^2))	\frac{d}{dx}(-\frac{3}{(1+3x)^{2}})
derivative of (x^2-2x+5)sqrt(25-x^2)	derivative\:(x^{2}-2x+5)\sqrt{25-x^{2}}
derivative of-5x^{1/2}+x^{3/2}	derivative\:-5x^{\frac{1}{2}}+x^{\frac{3}{2}}
integral of \sqrt[3]{x}+1/(sqrt(x))	\int\:\sqrt[3]{x}+\frac{1}{\sqrt{x}}dx
inverse oflaplace (s^2-1)/(s(s+2)(s-3))	inverselaplace\:\frac{s^{2}-1}{s(s+2)(s-3)}
derivative of-e^{xy}	\frac{d}{dx}(-e^{xy})
area y=x^3-x,y=0	area\:y=x^{3}-x,y=0
area x=-2,x=2,y=8x,y=x^2-9	area\:x=-2,x=2,y=8x,y=x^{2}-9
derivative of log_{2}(x-1)	\frac{d}{dx}(\log_{2}(x-1))
limit as x approaches-4+of 2/(x^2-16)	\lim\:_{x\to\:-4+}(\frac{2}{x^{2}-16})
integral of sin^2(x)cos^3(x	\int\:\sin^{2}(x)\cos^{3}(d)xdx
derivative of ln^2(8x^2)	derivative\:\ln^{2}(8x^{2})
integral of 1/2 ln\|x^2+1\|	\int\:\frac{1}{2}\ln\left\|x^{2}+1\right\|dx
integral of (sin(x))/(cos^2(x)+1)	\int\:\frac{\sin(x)}{\cos^{2}(x)+1}dx

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