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Popular Calculus Problems

(\partial)/(\partial x)(2x+6)	\frac{\partial\:}{\partial\:x}(2x+6)
limit as x approaches 0+of (((1+x)^{1/x})/e)^{1/x}	\lim\:_{x\to\:0+}((\frac{(1+x)^{\frac{1}{x}}}{e})^{\frac{1}{x}})
integral of 1/(xsqrt(6-x^2))	\int\:\frac{1}{x\sqrt{6-x^{2}}}dx
integral of sin^3(x/2)	\int\:\sin^{3}(\frac{x}{2})dx
limit as h approaches 0 of ((a^{u+h}-a^u))/h	\lim\:_{h\to\:0}(\frac{(a^{u+h}-a^{u})}{h})
integral of e^{-ax}sin(bx)	\int\:e^{-ax}\sin(bx)dx
integral of (e^{3x}+5e^{-x})	\int\:(e^{3x}+5e^{-x})dx
derivative of c_{1}cos(x+c_{2}sin(x))	\frac{d}{dx}(c_{1}\cos(x)+c_{2}\sin(x))
y^{''}-4y^'+4y=0	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=0
integral of x/(sqrt(7x^2+3))	\int\:\frac{x}{\sqrt{7x^{2}+3}}dx
derivative of ln(x^3-1/x)	\frac{d}{dx}(\ln(x^{3}-\frac{1}{x}))
f(x)=(xcos(x)+pi)/(pi-x)	f(x)=\frac{x\cos(x)+π}{π-x}
tangent of sqrt(5x+6)	tangent\:\sqrt{5x+6}
(\partial)/(\partial x)(-(8x-4y)/(-5x-9y))	\frac{\partial\:}{\partial\:x}(-\frac{8x-4y}{-5x-9y})
derivative of \sqrt[6]{3+tan(t)}	derivative\:\sqrt[6]{3+\tan(t)}
derivative of (2x^5-15/(x^4))	\frac{d}{dx}(\frac{2x^{5}-15}{x^{4}})
limit as x approaches-1 of \sqrt[3]{x}	\lim\:_{x\to\:-1}(\sqrt[3]{x})
derivative of e^{6y}	derivative\:e^{6y}
derivative of sin(3x+cos(2x))	\frac{d}{dx}(\sin(3x)+\cos(2x))
integral from 0 to 1 of (2x^2)/(1+x^2)	\int\:_{0}^{1}\frac{2x^{2}}{1+x^{2}}dx
derivative of 1-x^2	derivative\:1-x^{2}
limit as x approaches 0 of x^6cos(3/x)	\lim\:_{x\to\:0}(x^{6}\cos(\frac{3}{x}))
(dQ)/(dt)=-5/(980-\frac{3t){10}}Q+14.1	\frac{dQ}{dt}=-\frac{5}{980-\frac{3t}{10}}Q+14.1
integral from 4 to 5 of 1/x	\int\:_{4}^{5}\frac{1}{x}dx
integral of sqrt(9-x)	\int\:\sqrt{9-x}dx
(\partial)/(\partial x)(3x^3)	\frac{\partial\:}{\partial\:x}(3x^{3})
derivative of f(x)=-4/(x^2)	derivative\:f(x)=-\frac{4}{x^{2}}
tangent of y=8e^xcos(x)	tangent\:y=8e^{x}\cos(x)
integral of (sin(2x))^2cos(2x)	\int\:(\sin(2x))^{2}\cos(2x)dx
derivative of-4sin(4t)	derivative\:-4\sin(4t)
d/(dθ)(6sin(θ)-8cos(θ))	\frac{d}{dθ}(6\sin(θ)-8\cos(θ))
integral of 2x^{-2}	\int\:2x^{-2}dx
derivative of ln(4z+1)	derivative\:\ln(4z+1)
limit as x approaches 1 of 3x^3-4x^2+x+5	\lim\:_{x\to\:1}(3x^{3}-4x^{2}+x+5)
integral from-1 to 0 of (2x+3)^2	\int\:_{-1}^{0}(2x+3)^{2}dx
integral of e^{1/x} 1/(x^3)	\int\:e^{\frac{1}{x}}\frac{1}{x^{3}}dx
y^{''}-4y^'+3y=t^2	y^{\prime\:\prime\:}-4y^{\prime\:}+3y=t^{2}
derivative of (e^{-x}-xe^{-x}/(e^x))	\frac{d}{dx}(\frac{e^{-x}-xe^{-x}}{e^{x}})
laplacetransform e^{-0.75t}*cos(4t)	laplacetransform\:e^{-0.75t}\cdot\:\cos(4t)
derivative of 3^{(1-3x})	\frac{d}{dx}(3^{(1-3x)})
inverse oflaplace 20+(10)/s*1/(8s+1)	inverselaplace\:20+\frac{10}{s}\cdot\:\frac{1}{8s+1}
integral of 1/(y^2sqrt(y^2-7))	\int\:\frac{1}{y^{2}\sqrt{y^{2}-7}}dy
derivative of (sin(2x)cos(3x))/x	derivative\:\frac{\sin(2x)\cos(3x)}{x}
derivative of sin(x)tan(x)	derivative\:\sin(x)\tan(x)
integral from 1 to 16 of 1/(2x)	\int\:_{1}^{16}\frac{1}{2x}dx
integral of (-x+8)/(-x^2-x+8)	\int\:\frac{-x+8}{-x^{2}-x+8}dx
limit as x approaches 1 of (1+x)/(1-x)	\lim\:_{x\to\:1}(\frac{1+x}{1-x})
taylor 1/(1+1x)	taylor\:\frac{1}{1+1x}
y^'+ty=t	y^{\prime\:}+ty=t
derivative of x^2-3	derivative\:x^{2}-3
y^'+1/x y= 1/(x^2)	y^{\prime\:}+\frac{1}{x}y=\frac{1}{x^{2}}
taylor ln(3x-2)	taylor\:\ln(3x-2)
integral of 3/(sqrt(x))	\int\:\frac{3}{\sqrt{x}}dx
derivative of ln(sqrt((4x-4)/(5x+9)))	derivative\:\ln(\sqrt{\frac{4x-4}{5x+9}})
xy^'-3y=6	xy^{\prime\:}-3y=6
(\partial)/(\partial x)(e^{x^2+2y})	\frac{\partial\:}{\partial\:x}(e^{x^{2}+2y})
area y=10x,y=x^2	area\:y=10x,y=x^{2}
slope of 3x^2+24x-y^2+2y=-44	slope\:3x^{2}+24x-y^{2}+2y=-44
derivative of 1+tan(x)	\frac{d}{dx}(1+\tan(x))
integral from 0 to 4 of e^x	\int\:_{0}^{4}e^{x}dx
integral from-2 to 0 of sqrt(1+(-4)^2)	\int\:_{-2}^{0}\sqrt{1+(-4)^{2}}dx
derivative of y=cos(cos(cos(x)))	derivative\:y=\cos(\cos(\cos(x)))
(\partial)/(\partial x)(9+xln(xy-7))	\frac{\partial\:}{\partial\:x}(9+x\ln(xy-7))
area-x^2-3x,[-4,4]	area\:-x^{2}-3x,[-4,4]
integral of (x+8)/x	\int\:\frac{x+8}{x}dx
integral of 1/((x+1)^4)	\int\:\frac{1}{(x+1)^{4}}dx
integral of sin^3(5x)	\int\:\sin^{3}(5x)dx
integral of 1/(x(x^2-4)^{3/2)}	\int\:\frac{1}{x(x^{2}-4)^{\frac{3}{2}}}dx
integral from 0 to 20 of sqrt(4+3x)	\int\:_{0}^{20}\sqrt{4+3x}dx
y^{''}-3y^'-4y=-3,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}-3y^{\prime\:}-4y=-3,y(0)=0,y^{\prime\:}(0)=0
integral of tan^2(2xse)c^22x	\int\:\tan^{2}(2xse)c^{2}2x
y^'+y-2cos(x)=0	y^{\prime\:}+y-2\cos(x)=0
integral of sin((npix)/3)	\int\:\sin(\frac{nπx}{3})dx
sum from n=0 to infinity of 1/(n+3)	\sum\:_{n=0}^{\infty\:}\frac{1}{n+3}
integral of 1/(2x^5)	\int\:\frac{1}{2x^{5}}dx
limit as x approaches 0 of 4-x^2	\lim\:_{x\to\:0}(4-x^{2})
taylor (x+xcos(x)-2sin(x))/(x^3)	taylor\:\frac{x+x\cdot\:\cos(x)-2\cdot\:\sin(x)}{x^{3}}
d/(d{x)}(2{x}^4+2{y}^4+{z}^4-2{x}^2{y}^2{z})	\frac{d}{d{x}}(2{x}^{4}+2{y}^{4}+{z}^{4}-2{x}^{2}{y}^{2}{z})
integral of-3/y	\int\:-\frac{3}{y}dy
inverse oflaplace 3/((s+1)^2+9)	inverselaplace\:\frac{3}{(s+1)^{2}+9}
derivative of tan(13x)	\frac{d}{dx}(\tan(13x))
derivative of 2e^{4x}cos(5x)	derivative\:2e^{4x}\cos(5x)
(\partial)/(\partial x)(ln(x^7-y^3))	\frac{\partial\:}{\partial\:x}(\ln(x^{7}-y^{3}))
derivative of-5/(\sqrt[3]{x})	\frac{d}{dx}(-\frac{5}{\sqrt[3]{x}})
extreme f(x)=e^{a/x}	extreme\:f(x)=e^{\frac{a}{x}}
integral of (-2x^4)/((1-x)^3)	\int\:\frac{-2x^{4}}{(1-x)^{3}}dx
maclaurin sin(x^3)	maclaurin\:\sin(x^{3})
f(t)=sqrt(2)t	f(t)=\sqrt{2}t
limit as x approaches 1 of (x-1)/(x^6-1)	\lim\:_{x\to\:1}(\frac{x-1}{x^{6}-1})
y^{''}+4y=t^2	y^{\prime\:\prime\:}+4y=t^{2}
derivative of f(x)=e^{infinity}	derivative\:f(x)=e^{\infty\:}
derivative of (5x^2-2x+4)(4x^2+3x-6)	derivative\:(5x^{2}-2x+4)(4x^{2}+3x-6)
integral of-x^2+6	\int\:-x^{2}+6dx
limit as x approaches 5 of 1/((x-5))	\lim\:_{x\to\:5}(\frac{1}{(x-5)})
(\partial)/(\partial x)(x^2 1/(y+1))	\frac{\partial\:}{\partial\:x}(x^{2}\frac{1}{y+1})
tangent of y=(5x)/(x-3),(4,20)	tangent\:y=\frac{5x}{x-3},(4,20)
integral of (x^2+2y)	\int\:(x^{2}+2y)dx
area sqrt(x-2),14-x,2	area\:\sqrt{x-2},14-x,2
integral of (1-x)cos(npix)	\int\:(1-x)\cos(nπx)dx
inverse oflaplace (5s)/(s^2+4)	inverselaplace\:\frac{5s}{s^{2}+4}

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