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Popular Calculus Problems

sum from n=10000 to infinity of 1/n	\sum\:_{n=10000}^{\infty\:}\frac{1}{n}
integral of (x-arctan(2x))/(1+4x^2)	\int\:\frac{x-\arctan(2x)}{1+4x^{2}}dx
integral of log_{3}(\sqrt[5]{2x})	\int\:\log_{3}(\sqrt[5]{2x})dx
derivative of cos(x+cos(y))	\frac{d}{dx}(\cos(x)+\cos(y))
derivative of (sqrt(x)/(3+x))	\frac{d}{dx}(\frac{\sqrt{x}}{3+x})
integral of (x^2)/((1+x^2))	\int\:\frac{x^{2}}{(1+x^{2})}dx
(dy)/(dt)+y=2	\frac{dy}{dt}+y=2
integral of (6x+6)/(5x^2+26x+5)	\int\:\frac{6x+6}{5x^{2}+26x+5}dx
derivative of 3x^2+2x	\frac{d}{dx}(3x^{2}+2x)
(\partial)/(\partial x)(sin(x^3+y^2))	\frac{\partial\:}{\partial\:x}(\sin(x^{3}+y^{2}))
y^'+5y=1	y^{\prime\:}+5y=1
slope of (-3,2),(5,-4)	slope\:(-3,2),(5,-4)
limit as x approaches-1 of x^2+x+1	\lim\:_{x\to\:-1}(x^{2}+x+1)
derivative of (x^2/((1+x)))	\frac{d}{dx}(\frac{x^{2}}{(1+x)})
d/(dt)(e^{3t})	\frac{d}{dt}(e^{3t})
limit as x approaches-4 of-7	\lim\:_{x\to\:-4}(-7)
laplacetransform 6e^{-2t}	laplacetransform\:6e^{-2t}
d/(dy)(ln(cos(x/(y^2))))	\frac{d}{dy}(\ln(\cos(\frac{x}{y^{2}})))
integral of ln(x^n)	\int\:\ln(x^{n})dx
integral of (sec^4(x))/(tan^5(x))	\int\:\frac{\sec^{4}(x)}{\tan^{5}(x)}dx
slope of (3/10 ,-1/2),(1/5 , 1/5)	slope\:(\frac{3}{10},-\frac{1}{2}),(\frac{1}{5},\frac{1}{5})
(\partial)/(\partial x)(y^3sin(5x))	\frac{\partial\:}{\partial\:x}(y^{3}\sin(5x))
derivative of \sqrt[3]{1+8x}	derivative\:\sqrt[3]{1+8x}
derivative of z/(z+d/z)	derivative\:\frac{z}{z+\frac{d}{z}}
derivative of sqrt(ln(4x))	derivative\:\sqrt{\ln(4x)}
(\partial)/(\partial y)(2x-2xy)	\frac{\partial\:}{\partial\:y}(2x-2xy)
f^'(x)=x^{1/3}(2x-1)(x+1)	f^{\prime\:}(x)=x^{\frac{1}{3}}(2x-1)(x+1)
tangent of f(x)=2sqrt(x)+1,\at x= 1/4	tangent\:f(x)=2\sqrt{x}+1,\at\:x=\frac{1}{4}
integral of 4e^{x/2}	\int\:4e^{\frac{x}{2}}dx
derivative of (2^{2/3}-x^{2/3}^{3/2})	\frac{d}{dx}((2^{\frac{2}{3}}-x^{\frac{2}{3}})^{\frac{3}{2}})
derivative of (x^{e^x}/(1+x^2))	\frac{d}{dx}(\frac{x^{e^{x}}}{1+x^{2}})
derivative of sin(e^{sqrt(x)})	\frac{d}{dx}(\sin(e^{\sqrt{x}}))
d/(dθ)(e^{2θ})	\frac{d}{dθ}(e^{2θ})
integral of 1/(x(ln(x^2)))	\int\:\frac{1}{x(\ln(x^{2}))}dx
integral of ln(e^{xy}cos(x))	\int\:\ln(e^{xy}\cos(x))dy
integral of x^4sqrt(ax^5-b)	\int\:x^{4}\sqrt{ax^{5}-b}dx
(\partial)/(\partial x)(ln(x+6y+9z))	\frac{\partial\:}{\partial\:x}(\ln(x+6y+9z))
integral from 0 to pi/2 of tan(x/2)	\int\:_{0}^{\frac{π}{2}}\tan(\frac{x}{2})dx
25y^{''}-40y^'+16y=0,y(0)=4,y^'(0)=-5	25y^{\prime\:\prime\:}-40y^{\prime\:}+16y=0,y(0)=4,y^{\prime\:}(0)=-5
integral of ln(x^{1/2})	\int\:\ln(x^{\frac{1}{2}})dx
inverse oflaplace s/((s-1)^2)	inverselaplace\:\frac{s}{(s-1)^{2}}
(\partial)/(\partial x)(e^{e^x})	\frac{\partial\:}{\partial\:x}(e^{e^{x}})
d/(dθ)(sin(θ)+cos(θ))	\frac{d}{dθ}(\sin(θ)+\cos(θ))
integral of 8x-9	\int\:8x-9dx
integral of (x+4)cos(npix)	\int\:(x+4)\cos(nπx)dx
integral from 1 to 4 of 1/(w^2)	\int\:_{1}^{4}\frac{1}{w^{2}}dw
integral of (x+2)^2(1-x)^6	\int\:(x+2)^{2}(1-x)^{6}dx
area 5-x^2,sin(x),0,2	area\:5-x^{2},\sin(x),0,2
(d^4)/(dx^4)(8e^{-2x})	\frac{d^{4}}{dx^{4}}(8e^{-2x})
(dy)/(dx)=(x-2)e^{2y}	\frac{dy}{dx}=(x-2)e^{2y}
tangent of y=(6x^2-6x+2)(1+2x),\at x=1	tangent\:y=(6x^{2}-6x+2)(1+2x),\at\:x=1
(\partial)/(\partial y)(cos(x^2+y^3))	\frac{\partial\:}{\partial\:y}(\cos(x^{2}+y^{3}))
laplacetransform sin^2(7t)	laplacetransform\:\sin^{2}(7t)
derivative of-1/3	\frac{d}{dx}(-\frac{1}{3})
integral of cos^{16}(x)sin(x)	\int\:\cos^{16}(x)\sin(x)dx
derivative of (x^2-1^4(2-3x))	\frac{d}{dx}((x^{2}-1)^{4}(2-3x))
derivative of (x+1^{2/3})	\frac{d}{dx}((x+1)^{\frac{2}{3}})
(\partial)/(\partial x)(x^2-x-12y+1)	\frac{\partial\:}{\partial\:x}(x^{2}-x-12y+1)
derivative of 524.8*x^{0.75}	\frac{d}{dx}(524.8\cdot\:x^{0.75})
derivative of 5ln(2x)	\frac{d}{dx}(5\ln(2x))
integral from 0 to 3pi of 7x^2sin(1/6 x)	\int\:_{0}^{3π}7x^{2}\sin(\frac{1}{6}x)dx
derivative of y= x/9-9/x	derivative\:y=\frac{x}{9}-\frac{9}{x}
derivative of 3+3cos(x)	\frac{d}{dx}(3+3\cos(x))
integral of 15xsqrt(1-x)	\int\:15x\sqrt{1-x}dx
integral of 1/((x^2+6x+13))	\int\:\frac{1}{(x^{2}+6x+13)}dx
derivative of 2^{sqrt(x^2+3x+4)}	\frac{d}{dx}(2^{\sqrt{x^{2}+3x+4}})
derivative of x^3-3x	derivative\:x^{3}-3x
derivative of x9^x	\frac{d}{dx}(x9^{x})
derivative of ax^{a-1}ln(x+x^{a-1})	\frac{d}{dx}(ax^{a-1}\ln(x)+x^{a-1})
derivative of-(6e^{6/x})/(x^2)	derivative\:-\frac{6e^{\frac{6}{x}}}{x^{2}}
derivative of (5x^2/(2sqrt(b^2+x^2)))	\frac{d}{dx}(\frac{5x^{2}}{2\sqrt{b^{2}+x^{2}}})
(y^2+xy)dx+x^2dy=0	(y^{2}+xy)dx+x^{2}dy=0
20y^{''}+11y^'-3y=0	20y^{\prime\:\prime\:}+11y^{\prime\:}-3y=0
d/(d{y)}(({z})/(({x)^2+{y}^2+{z}^2)^{3/2}})	\frac{d}{d{y}}(\frac{{z}}{({x}^{2}+{y}^{2}+{z}^{2})^{\frac{3}{2}}})
limit as x approaches 1 of (x^2-3x+2)/(x^3-1)	\lim\:_{x\to\:1}(\frac{x^{2}-3x+2}{x^{3}-1})
integral of 3/(x^2sqrt(25-x^2))	\int\:\frac{3}{x^{2}\sqrt{25-x^{2}}}dx
f(x)= 2/(x+2)	f(x)=\frac{2}{x+2}
(\partial)/(\partial y)((x^2+y)e^{y/2})	\frac{\partial\:}{\partial\:y}((x^{2}+y)e^{\frac{y}{2}})
integral of e^{-2x}sin(2x)	\int\:e^{-2x}\sin(2x)dx
integral of (x^4)/(x^2+1)	\int\:\frac{x^{4}}{x^{2}+1}dx
integral from 1 to 3 of (x-1)ln(x)	\int\:_{1}^{3}(x-1)\ln(x)dx
derivative of 4/3 {p}(xi{r}(x)(x)^3)	\frac{d}{dx}(\frac{4}{3}{p}(x)i{r}(x)(x)^{3})
(\partial)/(\partial x)(yln(x^4+y^3+2)-7)	\frac{\partial\:}{\partial\:x}(y\ln(x^{4}+y^{3}+2)-7)
derivative of (4/3)pix^3	derivative\:(\frac{4}{3})pix^{3}
derivative of (x^3+2x^4)	\frac{d}{dx}((x^{3}+2x)^{4})
f(x)=((x-1)^2)/((x+2))	f(x)=\frac{(x-1)^{2}}{(x+2)}
implicit xsin(y)+ysin(x)=6	implicit\:x\sin(y)+y\sin(x)=6
y^'+5xe^y=0	y^{\prime\:}+5xe^{y}=0
(\partial)/(\partial x)(2ycos(9y^2x))	\frac{\partial\:}{\partial\:x}(2y\cos(9y^{2}x))
limit as x approaches 0 of x^{1/2}	\lim\:_{x\to\:0}(x^{\frac{1}{2}})
integral of 2xtan(x)	\int\:2x\tan(x)dx
limit as x approaches 2-of sqrt(4-x^2)	\lim\:_{x\to\:2-}(\sqrt{4-x^{2}})
sum from n=0 to infinity of 6/(n^2-1)	\sum\:_{n=0}^{\infty\:}\frac{6}{n^{2}-1}
laplacetransform-5t^3	laplacetransform\:-5t^{3}
(y^')/(1+y^2)+t/(e^{t^2)}=0,y(0)=1	\frac{y^{\prime\:}}{1+y^{2}}+\frac{t}{e^{t^{2}}}=0,y(0)=1
derivative of (11/x)	\frac{d}{dx}(\frac{11}{x})
integral of 2x(x^2-7)^6	\int\:2x(x^{2}-7)^{6}dx
derivative of \sqrt[7]{x^2}+2sqrt(x^7)	derivative\:\sqrt[7]{x^{2}}+2\sqrt{x^{7}}
integral from 1/7 to 3 of 12xln(7x)	\int\:_{\frac{1}{7}}^{3}12x\ln(7x)dx
derivative of (sin(x)/(x^3))	\frac{d}{dx}(\frac{\sin(x)}{x^{3}})

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