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Popular Calculus Problems

(\partial)/(\partial x)(e^{xy}+x^2z)	\frac{\partial\:}{\partial\:x}(e^{xy}+x^{2}z)
integral of cos^2(θ)	\int\:\cos^{2}(θ)dθ
(d^2)/(dx^2)f(x)= 7/(sqrt(x+4)),\at x=0	\frac{d^{2}}{dx^{2}}f(x)=\frac{7}{\sqrt{x+4}},\at\:x=0
sum from n=1 to infinity of (n^2)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{n^{2}}{n!}
3x^2e^y+(x^3e^y-1)(dy)/(dx)=0	3x^{2}e^{y}+(x^{3}e^{y}-1)\frac{dy}{dx}=0
tangent of f(x)=xsin(pix),\at x=1	tangent\:f(x)=x\sin(πx),\at\:x=1
tangent of f(x)= 3/(sqrt(x)),\at x= 1/4	tangent\:f(x)=\frac{3}{\sqrt{x}},\at\:x=\frac{1}{4}
4x-3y+y^'(2y-3x)=0	4x-3y+y^{\prime\:}(2y-3x)=0
limit as t approaches 0 of 4/t-4/(t^2-t)	\lim\:_{t\to\:0}(\frac{4}{t}-\frac{4}{t^{2}-t})
(\partial)/(\partial x)(-3x-1e^xcos(y))	\frac{\partial\:}{\partial\:x}(-3x-1e^{x}\cos(y))
integral of xe^{-x^2}	\int\:xe^{-x^{2}}dx
integral of (y+1)/y	\int\:\frac{y+1}{y}dy
derivative of f(x)= 1/(x+2)	derivative\:f(x)=\frac{1}{x+2}
(\partial)/(\partial x)(x/(3+y))	\frac{\partial\:}{\partial\:x}(\frac{x}{3+y})
integral of 1/(x^2+5x+4)	\int\:\frac{1}{x^{2}+5x+4}dx
limit as x approaches 5 of sqrt(x-9)	\lim\:_{x\to\:5}(\sqrt{x-9})
partialfraction x/(2x+1)	partialfraction\:\frac{x}{2x+1}
integral of (log_{10}(x^2))/x	\int\:\frac{\log_{10}(x^{2})}{x}dx
integral of 4x^2-2*x	\int\:4x^{2}-2\cdot\:xdx
integral from 0 to 7 of pi(x+1)^2	\int\:_{0}^{7}π(x+1)^{2}dx
derivative of f(x)=x^2-5x+3	derivative\:f(x)=x^{2}-5x+3
-3y^'+(3y)/x =(y^4)/(x^2)	-3y^{\prime\:}+\frac{3y}{x}=\frac{y^{4}}{x^{2}}
(\partial)/(\partial y)(3x^2y^2+4)	\frac{\partial\:}{\partial\:y}(3x^{2}y^{2}+4)
(\partial)/(\partial x)(-8(x+y+z)^2)	\frac{\partial\:}{\partial\:x}(-8(x+y+z)^{2})
integral of (arcsin(x))/((1-x^2)^{1/2)}	\int\:\frac{\arcsin(x)}{(1-x^{2})^{\frac{1}{2}}}dx
limit as x approaches 0 of x^{15x}	\lim\:_{x\to\:0}(x^{15x})
integral of (x^3)/(6-x^4)	\int\:\frac{x^{3}}{6-x^{4}}dx
derivative of (6u^2)/((u^2+u)^3)	derivative\:\frac{6u^{2}}{(u^{2}+u)^{3}}
laplacetransform [\delta(t+1)]	laplacetransform\:[\delta(t+1)]
integral of (-x+2)/(x^2-x+1)	\int\:\frac{-x+2}{x^{2}-x+1}dx
integral of sech(1/4)xtanh(1/4)x	\int\:\sech(\frac{1}{4})x\tanh(\frac{1}{4})xdx
inverse oflaplace (3s^2)/((s^2+4)^2)	inverselaplace\:\frac{3s^{2}}{(s^{2}+4)^{2}}
integral of 1/(sqrt(-x^2+4x+5))	\int\:\frac{1}{\sqrt{-x^{2}+4x+5}}dx
(\partial)/(\partial x)(r+2r^4x+4x)	\frac{\partial\:}{\partial\:x}(r+2r^{4}x+4x)
(4+y^2)dx+(9+x^2)dy=0	(4+y^{2})dx+(9+x^{2})dy=0
integral of (x^4+2x+6)/(x^3+x^2-2x)	\int\:\frac{x^{4}+2x+6}{x^{3}+x^{2}-2x}dx
integral of (11)/(11+e^x)	\int\:\frac{11}{11+e^{x}}dx
d/(dt)(tan(e^{2t})+e^{tan(2t)})	\frac{d}{dt}(\tan(e^{2t})+e^{\tan(2t)})
limit as x approaches 0-of 1/x-1/(\|x\|)	\lim\:_{x\to\:0-}(\frac{1}{x}-\frac{1}{\left\|x\right\|})
derivative of x^3-2x^2+x+1	\frac{d}{dx}(x^{3}-2x^{2}+x+1)
(\partial)/(\partial x)((e^x)/(y+x^3))	\frac{\partial\:}{\partial\:x}(\frac{e^{x}}{y+x^{3}})
derivative of tan(pi/4)	\frac{d}{dx}(\tan(\frac{π}{4}))
integral of (x^3)/((x^2+4)^2)	\int\:\frac{x^{3}}{(x^{2}+4)^{2}}dx
limit as x approaches infinity of x^8	\lim\:_{x\to\:\infty\:}(x^{8})
integral of (1-x^2)/(1+x^2)	\int\:\frac{1-x^{2}}{1+x^{2}}dx
integral of 4x-15x^2+e^x	\int\:4x-15x^{2}+e^{x}dx
(\partial)/(\partial y)(2x^3)	\frac{\partial\:}{\partial\:y}(2x^{3})
integral of (4x)/((x-1)^2(x+1))	\int\:\frac{4x}{(x-1)^{2}(x+1)}dx
derivative of (x^2+3^5)	\frac{d}{dx}((x^{2}+3)^{5})
derivative of f(x)=(sin(x))^2	derivative\:f(x)=(\sin(x))^{2}
area x^2+1,0,2	area\:x^{2}+1,0,2
(\partial)/(\partial x)(f(x,y)(xy))	\frac{\partial\:}{\partial\:x}(f(x,y)(xy))
limit as x approaches 0-of (4-x)/x	\lim\:_{x\to\:0-}(\frac{4-x}{x})
integral of (x^2+1)/(x(x-1)^3)	\int\:\frac{x^{2}+1}{x(x-1)^{3}}dx
integral of sin(3x)sin(2x)	\int\:\sin(3x)\sin(2x)dx
derivative of x^2-8x+16	derivative\:x^{2}-8x+16
integral from 2 to infinity of 1/(x^3)	\int\:_{2}^{\infty\:}\frac{1}{x^{3}}dx
y^'-2y=3e^t	y^{\prime\:}-2y=3e^{t}
derivative of 15000+2500^t	derivative\:15000+2500^{t}
(\partial)/(\partial x)(2/(1+x^3))	\frac{\partial\:}{\partial\:x}(\frac{2}{1+x^{3}})
integral of xln^2(x	\int\:x\ln^{2}(d)xdx
derivative of arccot(sqrt(x^2))	\frac{d}{dx}(\arccot(\sqrt{x^{2}}))
derivative of 3e^{-5x}	\frac{d}{dx}(3e^{-5x})
derivative of f(x)=x^3-12x^2+45x	derivative\:f(x)=x^{3}-12x^{2}+45x
integral of (x^2)/(2x-1)	\int\:\frac{x^{2}}{2x-1}dx
integral of sqrt(x(4-x))	\int\:\sqrt{x(4-x)}dx
tangent of f(x)=(x/(1+x))^5,\at x=1	tangent\:f(x)=(\frac{x}{1+x})^{5},\at\:x=1
laplacetransform 8^t*t+10	laplacetransform\:8^{t}\cdot\:t+10
d/(dy)(tan(x^2+y))	\frac{d}{dy}(\tan(x^{2}+y))
derivative of sqrt(x^3-4)	derivative\:\sqrt{x^{3}-4}
integral of e^{2xy}	\int\:e^{2xy}dx
integral of cos(2x)cos(x)	\int\:\cos(2x)\cos(x)dx
integral of x/((x^4+1))	\int\:\frac{x}{(x^{4}+1)}dx
derivative of sqrt(x)-5\sqrt[3]{x}	derivative\:\sqrt{x}-5\sqrt[3]{x}
derivative of (1-2x^2)/(x^4-2x^2+6)	derivative\:\frac{1-2x^{2}}{x^{4}-2x^{2}+6}
limit as h approaches 0 of ((f(h)(0+h)-f(0)))/h	\lim\:_{h\to\:0}(\frac{(f(h)(0+h)-f(0))}{h})
integral of xf(x)	\int\:xf(x)dx
f(x)=17e^x	f(x)=17e^{x}
tangent of f(x)=-x^2+4x,\at x=1	tangent\:f(x)=-x^{2}+4x,\at\:x=1
(xdy)/(dx)+5y=x^3-x	\frac{xdy}{dx}+5y=x^{3}-x
integral from 0 to 1 of (e^x+1)/(e^x+x)	\int\:_{0}^{1}\frac{e^{x}+1}{e^{x}+x}dx
y^'=ysin(x),y(0)=1	y^{\prime\:}=y\sin(x),y(0)=1
1/6 y^{''}+6y=tan(6t)-1/2 e^{3t}	\frac{1}{6}y^{\prime\:\prime\:}+6y=\tan(6t)-\frac{1}{2}e^{3t}
(\partial)/(\partial x)(tan(y))	\frac{\partial\:}{\partial\:x}(\tan(y))
(dy)/(dx)=((2880-y))/(320)	\frac{dy}{dx}=\frac{(2880-y)}{320}
y^'+y=1,y(0)=1	y^{\prime\:}+y=1,y(0)=1
integral of (x^3+1)	\int\:(x^{3}+1)dx
integral of (sqrt(25x^2-4))/x	\int\:\frac{\sqrt{25x^{2}-4}}{x}dx
derivative of arccos(6x^2)	\frac{d}{dx}(\arccos(6x^{2}))
(\partial)/(\partial x)(arccos(xy))	\frac{\partial\:}{\partial\:x}(\arccos(xy))
(\partial)/(\partial x)(m/p+625 p/x)	\frac{\partial\:}{\partial\:x}(\frac{m}{p}+625\frac{p}{x})
derivative of e^{(3x^2/2})	\frac{d}{dx}(e^{\frac{3x^{2}}{2}})
(\partial)/(\partial x)((mcT)/(wp(m,T,w,x)))	\frac{\partial\:}{\partial\:x}(\frac{mcT}{wp(m,T,w,x)})
integral from 0 to pi of pi^{25}sin^2(x)	\int\:_{0}^{π}π^{25}\sin^{2}(x)dx
integral of 1	\int\:1dθ
integral from 0 to 9 of sqrt(1+x)	\int\:_{0}^{9}\sqrt{1+x}dx
sum from n=1 to infinity of arctan(n^2)	\sum\:_{n=1}^{\infty\:}\arctan(n^{2})
limit as x approaches infinity of \sqrt[5]{infinity ^3+1/7}	\lim\:_{x\to\:\infty\:}(\sqrt[5]{\infty\:^{3}+\frac{1}{7}})
limit as x approaches 0 of ((2^x-2^{-x}))/x	\lim\:_{x\to\:0}(\frac{(2^{x}-2^{-x})}{x})
derivative of sin^2((x+2/(x+1)))	\frac{d}{dx}(\sin^{2}(\frac{x+2}{x+1}))

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