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Popular Calculus Problems

integral from 0 to 1 of 6ln(x)	\int\:_{0}^{1}6\ln(x)dx
laplacetransform 3t^2-5e^{3t}	laplacetransform\:3t^{2}-5e^{3t}
limit as x approaches 2a of (x^2-2ax+a^2)/(x^3-a^3)	\lim\:_{x\to\:2a}(\frac{x^{2}-2ax+a^{2}}{x^{3}-a^{3}})
integral from 2 to 4 of 3x	\int\:_{2}^{4}3xdx
(\partial)/(\partial x)(arctan(2x))	\frac{\partial\:}{\partial\:x}(\arctan(2x))
limit as x approaches-1 of-1(x+1)	\lim\:_{x\to\:-1}(-1(x+1))
derivative of 7x+3	\frac{d}{dx}(7x+3)
derivative of-(192/(x^4))	\frac{d}{dx}(-\frac{192}{x^{4}})
tangent of (3+sin(2x))^2	tangent\:(3+\sin(2x))^{2}
integral of x^4y^5	\int\:x^{4}y^{5}dx
area y=7x^4-7x^2,y=5x^2	area\:y=7x^{4}-7x^{2},y=5x^{2}
limit as x approaches-1/2 of 2x^2+3x-1	\lim\:_{x\to\:-\frac{1}{2}}(2x^{2}+3x-1)
limit as x approaches-8+of 1/(x+8)	\lim\:_{x\to\:-8+}(\frac{1}{x+8})
(\partial)/(\partial y)(sin(x+y))	\frac{\partial\:}{\partial\:y}(\sin(x+y))
derivative of y=x^2+10x+21	derivative\:y=x^{2}+10x+21
integral of 9/(sqrt(81-9x^2))	\int\:\frac{9}{\sqrt{81-9x^{2}}}dx
derivative of 6ycos(x)	\frac{d}{dx}(6y\cos(x))
limit as x approaches 81 of log_{243}(x)	\lim\:_{x\to\:81}(\log_{243}(x))
limit as x approaches infinity of x^4-1	\lim\:_{x\to\:\infty\:}(x^{4}-1)
(\partial)/(\partial x)(x^y-y^x)	\frac{\partial\:}{\partial\:x}(x^{y}-y^{x})
tangent of 4x^2,\at x=3	tangent\:4x^{2},\at\:x=3
(\partial)/(\partial θ)(θ)	\frac{\partial\:}{\partial\:θ}(θ)
integral of 12x^2-sin(x)	\int\:12x^{2}-\sin(x)dx
x^2y^'-2x^3e^{(-1)/x}=y	x^{2}y^{\prime\:}-2x^{3}e^{\frac{-1}{x}}=y
integral of 4/(x(x^2+4)^2)	\int\:\frac{4}{x(x^{2}+4)^{2}}dx
derivative of 25+3x-x^2+5x^8	\frac{d}{dx}(25+3x-x^{2}+5x^{8})
derivative of f(x)= 3/(x^3)	derivative\:f(x)=\frac{3}{x^{3}}
integral of 7sec^3(2x)	\int\:7\sec^{3}(2x)dx
(dy)/(dx)+y^2-y=0	\frac{dy}{dx}+y^{2}-y=0
integral of (e^x+2)(x-5)	\int\:(e^{x}+2)(x-5)dx
derivative of y=ln(x^3sin^2(x))	derivative\:y=\ln(x^{3}\sin^{2}(x))
integral of x^7sqrt(x^4+2)	\int\:x^{7}\sqrt{x^{4}+2}dx
taylor 1/(x+5)	taylor\:\frac{1}{x+5}
derivative of y=34(3x+1)^{-2/5}	derivative\:y=34(3x+1)^{-\frac{2}{5}}
limit as x approaches-1 of x^4	\lim\:_{x\to\:-1}(x^{4})
derivative of ln\|1+x\|	\frac{d}{dx}(\ln\left\|1+x\right\|)
derivative of arcsec(x)-8x	derivative\:\arcsec(x)-8x
tangent of sin(x),\at x=(-pi/3)	tangent\:\sin(x),\at\:x=(-\frac{π}{3})
integral from 0 to pi/5 of xsin(10x)	\int\:_{0}^{\frac{π}{5}}x\sin(10x)dx
integral of \sqrt[7]{x}+1/(\sqrt[7]{x)}	\int\:\sqrt[7]{x}+\frac{1}{\sqrt[7]{x}}dx
integral from 0 to sqrt(t of)xe^{-x^2}	\int\:_{0}^{\sqrt{t}}xe^{-x^{2}}dx
((x^4)/8+1/(4x^2))^'	(\frac{x^{4}}{8}+\frac{1}{4x^{2}})^{\prime\:}
derivative of e^{(x^2/2}x)	\frac{d}{dx}(e^{\frac{x^{2}}{2}}x)
integral of e^{-3y}	\int\:e^{-3y}dy
limit as x approaches 6 of x+6	\lim\:_{x\to\:6}(x+6)
(d^2)/(dx^2)(1/(3+t))	\frac{d^{2}}{dx^{2}}(\frac{1}{3+t})
tangent of f(x)=x^2-x+1	tangent\:f(x)=x^{2}-x+1
derivative of 2/3 e^x+e^{-2x}	\frac{d}{dx}(\frac{2}{3}e^{x}+e^{-2x})
limit as x approaches 0 of 1-cos(x)	\lim\:_{x\to\:0}(1-\cos(x))
derivative of (x^{-2}+x^4-6/(3x^3+4x^4))	\frac{d}{dx}(\frac{x^{-2}+x^{4}-6}{3x^{3}+4x^{4}})
derivative of e^{(4x)}	derivative\:e^{(4x)}
integral of x^2sqrt(x^3+3)	\int\:x^{2}\sqrt{x^{3}+3}dx
(\partial)/(\partial y)(3y^2+10x^2y^2)	\frac{\partial\:}{\partial\:y}(3y^{2}+10x^{2}y^{2})
derivative of 4/(1+x^2)	derivative\:\frac{4}{1+x^{2}}
derivative of 1/e	\frac{d}{dx}(\frac{1}{e})
integral of 1/((e^{2x)+4)}	\int\:\frac{1}{(e^{2x}+4)}dx
(\partial)/(\partial y)(2xy+y^4)	\frac{\partial\:}{\partial\:y}(2xy+y^{4})
integral of (-x^2)/2	\int\:\frac{-x^{2}}{2}dx
integral from-pi to pi of x^2	\int\:_{-π}^{π}x^{2}dx
limit as x approaches 4 of x/(4-x)-x^3	\lim\:_{x\to\:4}(\frac{x}{4-x}-x^{3})
tangent of f(x)=3xcos(x),(pi,-3pi)	tangent\:f(x)=3x\cos(x),(π,-3π)
(1-e^{-x}-xe^{-x})^'	(1-e^{-x}-xe^{-x})^{\prime\:}
(\partial)/(\partial x)(x^3y-x)	\frac{\partial\:}{\partial\:x}(x^{3}y-x)
integral of (x^2+1)/(sqrt(x^3+3x))	\int\:\frac{x^{2}+1}{\sqrt{x^{3}+3x}}dx
integral of e^x*(-3)e^{e^x+2}	\int\:e^{x}\cdot\:(-3)e^{e^{x}+2}dx
derivative of x5^{2x}	\frac{d}{dx}(x5^{2x})
integral from 0 to sqrt(3 of)1	\int\:_{0}^{\sqrt{3}}1
integral of (sqrt(9+x^2))/(x^4)	\int\:\frac{\sqrt{9+x^{2}}}{x^{4}}dx
integral from 0 to 1 of (x^2+1)e^{2x}	\int\:_{0}^{1}(x^{2}+1)e^{2x}dx
tangent of 6x^2-4xy+4y^2-14=0,(1,2)	tangent\:6x^{2}-4xy+4y^{2}-14=0,(1,2)
tangent of y=sqrt(x+1),(8,3)	tangent\:y=\sqrt{x+1},(8,3)
derivative of f(x)=x^4-2x^3+x-1	derivative\:f(x)=x^{4}-2x^{3}+x-1
d/(dt)(e^{{r}(t)t})	\frac{d}{dt}(e^{{r}(t)t})
area-x^2+9x,x^2-5x	area\:-x^{2}+9x,x^{2}-5x
derivative of y=sqrt(3-5x)	derivative\:y=\sqrt{3-5x}
integral from 4 to 9 of 1/(8-sqrt(x))	\int\:_{4}^{9}\frac{1}{8-\sqrt{x}}dx
integral of e^{-xt}	\int\:e^{-xt}dx
derivative of 3ln(x+ln(y))	\frac{d}{dx}(3\ln(x)+\ln(y))
slope of (1,3),(-2,-3)	slope\:(1,3),(-2,-3)
(\partial)/(\partial y)(e^{x^2+y})	\frac{\partial\:}{\partial\:y}(e^{x^{2}+y})
(dy)/(dt)=8y,y(4)=4	\frac{dy}{dt}=8y,y(4)=4
inverse oflaplace 1/(2s)	inverselaplace\:\frac{1}{2s}
f(x)=cos(1/x)	f(x)=\cos(\frac{1}{x})
derivative of csc(sqrt(x^2-1))	\frac{d}{dx}(\csc(\sqrt{x^{2}-1}))
derivative of (3^2+5x)^4(2x-2)^3	derivative\:(3^{2}+5x)^{4}(2x-2)^{3}
(dy)/(dx)+y^3x+y=0	\frac{dy}{dx}+y^{3}x+y=0
derivative of-2cos(2x)	derivative\:-2\cos(2x)
derivative of f(x)=25^x	derivative\:f(x)=25^{x}
integral of 9/(15sin(x)-8cos(x))	\int\:\frac{9}{15\sin(x)-8\cos(x)}dx
derivative of (2x/(sqrt(a^2-x^2)))	\frac{d}{dx}(\frac{2x}{\sqrt{a^{2}-x^{2}}})
sum from n=1 to infinity of 1/(4n^2+7)	\sum\:_{n=1}^{\infty\:}\frac{1}{4n^{2}+7}
y^{''}+ay=0,y(0)=1,y(1)=0	y^{\prime\:\prime\:}+ay=0,y(0)=1,y(1)=0
slope of (8.2)(9.3)	slope\:(8.2)(9.3)
limit as x approaches-2 of (1+x)/(x^3+8)	\lim\:_{x\to\:-2}(\frac{1+x}{x^{3}+8})
derivative of 3xsqrt(3x^2+1)	derivative\:3x\sqrt{3x^{2}+1}
integral of (tan^2(y)+1)	\int\:(\tan^{2}(y)+1)dy
y^{''}-4y^'+40y=0	y^{\prime\:\prime\:}-4y^{\prime\:}+40y=0
integral of sqrt((3x+1)^2-2)	\int\:\sqrt{(3x+1)^{2}-2}dx
derivative of sin(2x+5)	\frac{d}{dx}(\sin(2x+5))
integral of e^{e^x}e^x	\int\:e^{e^{x}}e^{x}dx

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