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Popular Calculus Problems

integral of 4e^{3x}cos(5x)	\int\:4e^{3x}\cos(5x)dx
integral from 1 to 16 of \sqrt[4]{x}	\int\:_{1}^{16}\sqrt[4]{x}dx
derivative of ln(x+2)	derivative\:\ln(x+2)
integral from 0 to 1 of (5x)^2-(5x^4)^2	\int\:_{0}^{1}(5x)^{2}-(5x^{4})^{2}dx
derivative of y=(ln(x))^2	derivative\:y=(\ln(x))^{2}
limit as x approaches 0 of 2sin(x)	\lim\:_{x\to\:0}(2\sin(x))
(\partial}{\partial x}(5sin(\frac{5x)/y))	\frac{\partial\:}{\partial\:x}(5\sin(\frac{5x}{y}))
tangent of 2x^2+8x	tangent\:2x^{2}+8x
derivative of ((x-1(2x+3)+7)^5)	\frac{d}{dx}(((x-1)(2x+3)+7)^{5})
derivative of ax^2e^{-2x}	\frac{d}{dx}(ax^{2}e^{-2x})
integral of (3^x)/(4^x)	\int\:\frac{3^{x}}{4^{x}}dx
laplacetransform 1/2 e^{-4t}-1/2 e^{-6t}	laplacetransform\:\frac{1}{2}e^{-4t}-\frac{1}{2}e^{-6t}
limit as x approaches 0-of sin(x)	\lim\:_{x\to\:0-}(\sin(x))
x^2y^{''}+2xy^'-30y=0,y(1)=-5,y^'(1)=-6	x^{2}y^{\prime\:\prime\:}+2xy^{\prime\:}-30y=0,y(1)=-5,y^{\prime\:}(1)=-6
y^{''}+3y=x	y^{\prime\:\prime\:}+3y=x
integral of tln(t+3)	\int\:t\ln(t+3)dt
integral of 1/b sin(bx)	\int\:\frac{1}{b}\sin(bx)dx
integral of (2x-1)^6	\int\:(2x-1)^{6}dx
integral of (2ln(x))/(x^2)	\int\:\frac{2\ln(x)}{x^{2}}dx
normal of y=x^2-9x,(7,-14)	normal\:y=x^{2}-9x,(7,-14)
integral from-1 to 1 of 3x	\int\:_{-1}^{1}3xdx
limit as x approaches 0+of x^{15}ln(x)	\lim\:_{x\to\:0+}(x^{15}\ln(x))
derivative of f(x)=(1-3t)/(2+t)	derivative\:f(x)=\frac{1-3t}{2+t}
integral of (-3x+2)*e^{-x}	\int\:(-3x+2)\cdot\:e^{-x}dx
(\partial)/(\partial y)(x/(x^2+y^2)+x)	\frac{\partial\:}{\partial\:y}(\frac{x}{x^{2}+y^{2}}+x)
(\partial)/(\partial x)(x(x+y)2)	\frac{\partial\:}{\partial\:x}(x(x+y)2)
integral of e^x*cos(x)	\int\:e^{x}\cdot\:\cos(x)dx
limit as x approaches 0+of x^2+5	\lim\:_{x\to\:0+}(x^{2}+5)
integral from 0 to pi/6 of 8sec^3(x)	\int\:_{0}^{\frac{π}{6}}8\sec^{3}(x)dx
area 2/x ,8x, x/8	area\:\frac{2}{x},8x,\frac{x}{8}
limit as x approaches 5 of (20-4x)/(x-5)	\lim\:_{x\to\:5}(\frac{20-4x}{x-5})
integral from 0 to infinity of x^{-2}	\int\:_{0}^{\infty\:}x^{-2}dx
area x=2y^2,x+y=1	area\:x=2y^{2},x+y=1
integral from 0 to a of sin^2((npix)/a)	\int\:_{0}^{a}\sin^{2}(\frac{nπx}{a})dx
derivative of f(x)=-x^2+2	derivative\:f(x)=-x^{2}+2
derivative of 3/(2-3x)	\frac{d}{dx}(\frac{3}{2-3x})
tangent of f(x)=-1/x ,(3,-1/3)	tangent\:f(x)=-\frac{1}{x},(3,-\frac{1}{3})
(\partial)/(\partial x)(7xcos(3xy))	\frac{\partial\:}{\partial\:x}(7x\cos(3xy))
integral of (12x)/(\sqrt[3]{3-x^2)}	\int\:\frac{12x}{\sqrt[3]{3-x^{2}}}dx
(-5)^'	(-5)^{\prime\:}
integral from 5 to 8 of x/(x^2+4x+20)	\int\:_{5}^{8}\frac{x}{x^{2}+4x+20}dx
limit as x approaches infinity of x+2	\lim\:_{x\to\:\infty\:}(x+2)
(\partial)/(\partial x)(xy+y/x)	\frac{\partial\:}{\partial\:x}(xy+\frac{y}{x})
tangent of f(x)=sqrt(x-8),\at x=9	tangent\:f(x)=\sqrt{x-8},\at\:x=9
integral of 0.06e^{0.04x}	\int\:0.06e^{0.04x}dx
integral of 3x^2cos(x)	\int\:3x^{2}\cos(x)dx
sum from n=0 to infinity of (n!)/(107^n)	\sum\:_{n=0}^{\infty\:}\frac{n!}{107^{n}}
derivative of (x^2/(5x+2))	\frac{d}{dx}(\frac{x^{2}}{5x+2})
derivative of 3t^2-30t+72	derivative\:3t^{2}-30t+72
f(x)= 8/x	f(x)=\frac{8}{x}
limit as x approaches-1+of (2x)/(x+1)	\lim\:_{x\to\:-1+}(\frac{2x}{x+1})
derivative of x^2,x	\frac{d}{dx}(x^{2},x)
limit as x approaches 0+of 1/(1-2^{1/x)}	\lim\:_{x\to\:0+}(\frac{1}{1-2^{\frac{1}{x}}})
integral of sin(5pit)	\int\:\sin(5πt)dt
derivative of 3x+5/x	\frac{d}{dx}(3x+\frac{5}{x})
(dy)/(dx)=(10x)/(7y)	\frac{dy}{dx}=\frac{10x}{7y}
d/(dt)(1+t^3)	\frac{d}{dt}(1+t^{3})
derivative of-3cot(x)	derivative\:-3\cot(x)
integral of x/(sqrt(x+5))	\int\:\frac{x}{\sqrt{x+5}}dx
integral of 4/(sqrt(t))	\int\:\frac{4}{\sqrt{t}}dt
(\partial)/(\partial x)(2sqrt(xy))	\frac{\partial\:}{\partial\:x}(2\sqrt{xy})
derivative of f(g(x))	derivative\:f(g(x))
(\partial)/(\partial x)(x^{y^z})	\frac{\partial\:}{\partial\:x}(x^{y^{z}})
tangent of f(x)=sqrt(7x+1),\at x=5	tangent\:f(x)=\sqrt{7x+1},\at\:x=5
area 2sin(2x-pi),5sin(2x-3pi)	area\:2\sin(2x-π),5\sin(2x-3π)
integral of 1/((5+x)^2)	\int\:\frac{1}{(5+x)^{2}}dx
derivative of (x^2/((x-1)))	\frac{d}{dx}(\frac{x^{2}}{(x-1)})
integral of x^2+6e^x+C	\int\:x^{2}+6e^{x}+Cdx
integral of esqrt(x)	\int\:e\sqrt{x}dx
integral of (sin(2x))/(1-sin^2(x))	\int\:\frac{\sin(2x)}{1-\sin^{2}(x)}dx
y^{''}-y=(e^x)/(e^x)	y^{\prime\:\prime\:}-y=\frac{e^{x}}{e^{x}}
integral from 1 to 2 of sqrt(4-x^2)	\int\:_{1}^{2}\sqrt{4-x^{2}}dx
derivative of arctan(sin(3x))	\frac{d}{dx}(\arctan(\sin(3x)))
d/(dt)(((8t)^2)/(10))	\frac{d}{dt}(\frac{(8t)^{2}}{10})
sum from n=1 to infinity of x/(2^n)	\sum\:_{n=1}^{\infty\:}\frac{x}{2^{n}}
(dy)/(dx)= x/(ye^{y+x^2)}	\frac{dy}{dx}=\frac{x}{ye^{y+x^{2}}}
(\partial)/(\partial x)(sin(7x^5y-7xy^4))	\frac{\partial\:}{\partial\:x}(\sin(7x^{5}y-7xy^{4}))
limit as x approaches 0+of 6/x-6/(\|x\|)	\lim\:_{x\to\:0+}(\frac{6}{x}-\frac{6}{\left\|x\right\|})
integral of 1/(a+x)	\int\:\frac{1}{a+x}dx
integral from 0 to 2 of-x^2-x+13	\int\:_{0}^{2}-x^{2}-x+13dx
integral of (pi-x)sin(nx)	\int\:(π-x)\sin(nx)dx
((1-2ln(x))/(x^3))^'	(\frac{1-2\ln(x)}{x^{3}})^{\prime\:}
integral of (e^x)/(4-e^{2x)}	\int\:\frac{e^{x}}{4-e^{2x}}dx
derivative of (-2x^2+x+4)/(x^2+4x-1)	derivative\:\frac{-2x^{2}+x+4}{x^{2}+4x-1}
integral of (6-x)	\int\:(6-x)dx
integral from 0 to 3 of cos((pix)/3)	\int\:_{0}^{3}\cos(\frac{πx}{3})dx
limit as x approaches 0 of (1-x)^{5/x}	\lim\:_{x\to\:0}((1-x)^{\frac{5}{x}})
derivative of f(x)=sin^2(x^2)	derivative\:f(x)=\sin^{2}(x^{2})
integral of (x^4+x-4)/(x^2+2)	\int\:\frac{x^{4}+x-4}{x^{2}+2}dx
derivative of x/(sqrt(x^2+64))	\frac{d}{dx}(\frac{x}{\sqrt{x^{2}+64}})
(dy)/(dx)(x^2)=y^3	\frac{dy}{dx}(x^{2})=y^{3}
integral of 1/(\sqrt[3]{t^2)}	\int\:\frac{1}{\sqrt[3]{t^{2}}}dt
integral of (e^a+1)/(e^a)	\int\:\frac{e^{a}+1}{e^{a}}da
limit as x approaches-8 of (x^2-4)/(8-x)	\lim\:_{x\to\:-8}(\frac{x^{2}-4}{8-x})
integral of 1/(4e^{-4x)+e^{4x}}	\int\:\frac{1}{4e^{-4x}+e^{4x}}dx
limit as x approaches 0 of f(x)(x^2)	\lim\:_{x\to\:0}(f(x)(x^{2}))
(dx)/(dt)=1	\frac{dx}{dt}=1
tangent of y=x^2-x^4,(0,1)	tangent\:y=x^{2}-x^{4},(0,1)
y^'(x)=(3x^2)/(3y^2-4),y(1)=0	y^{\prime\:}(x)=\frac{3x^{2}}{3y^{2}-4},y(1)=0
laplacetransform sin(2t)-5t	laplacetransform\:\sin(2t)-5t

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