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Popular Calculus Problems

integral of xe^{-xy}	\int\:xe^{-xy}dy
(\partial)/(\partial x)(7xe^x)	\frac{\partial\:}{\partial\:x}(7xe^{x})
inverse oflaplace 1/((s^2(1+s)))	inverselaplace\:\frac{1}{(s^{2}(1+s))}
integral from 0 to pi of usin^2(u)	\int\:_{0}^{π}u\sin^{2}(u)du
(1+x^4)dy+(1+4y^2)dx=0	(1+x^{4})dy+(1+4y^{2})dx=0
y^'-5y^{(2)}e^{(-3x)}=0,y(0)=9	y^{\prime\:}-5y^{(2)}e^{(-3x)}=0,y(0)=9
integral of (x^3)/(x^2+2x+1)	\int\:\frac{x^{3}}{x^{2}+2x+1}dx
tangent of y=((x^2))/(8+sqrt(x))	tangent\:y=\frac{(x^{2})}{8+\sqrt{x}}
integral of ((1-x^3))/(x\sqrt[3]{x)}	\int\:\frac{(1-x^{3})}{x\sqrt[3]{x}}dx
integral of ae^{-mx}	\int\:ae^{-mx}dx
(dy)/(dx)+(3/x)y=-2x+7	\frac{dy}{dx}+(\frac{3}{x})y=-2x+7
limit as x approaches-1 of 1+2x	\lim\:_{x\to\:-1}(1+2x)
100y^{''}+60y^'-27y=0	100y^{\prime\:\prime\:}+60y^{\prime\:}-27y=0
derivative of (3\sqrt[3]{2}x^{5/3}/5)	\frac{d}{dx}(\frac{3\sqrt[3]{2}x^{\frac{5}{3}}}{5})
area 7x, 7/4 x,78-x^2,y=0	area\:7x,\frac{7}{4}x,78-x^{2},y=0
y^{''}+2y^'+26y=e^{-x}cos(5*x)	y^{\prime\:\prime\:}+2\cdot\:y^{\prime\:}+26\cdot\:y=e^{-x}\cos(5\cdot\:x)
integral of (8000-2000x)/((x^2-8x+17)^2)	\int\:\frac{8000-2000x}{(x^{2}-8x+17)^{2}}dx
derivative of x^5*tan(x)	\frac{d}{dx}(x^{5}\cdot\:\tan(x))
sum from n=1 to infinity of 1	\sum\:_{n=1}^{\infty\:}1
integral of (x^2)/(sqrt(36-25x^2))	\int\:\frac{x^{2}}{\sqrt{36-25x^{2}}}dx
integral from-2 to 3 of 9/(x^4)	\int\:_{-2}^{3}\frac{9}{x^{4}}dx
derivative of 4cos(sin(2x))	derivative\:4\cos(\sin(2x))
derivative of x^3+xy^2	\frac{d}{dx}(x^{3}+xy^{2})
derivative of e^{-x^5}	derivative\:e^{-x^{5}}
integral of (u+3)(8u+5)	\int\:(u+3)(8u+5)du
integral of (e^{4x})/((e^{2x)-1)^3}	\int\:\frac{e^{4x}}{(e^{2x}-1)^{3}}dx
limit as x approaches 2+of 1/((x-2)^3)	\lim\:_{x\to\:2+}(\frac{1}{(x-2)^{3}})
limit as x approaches 0 of x/(x^2-4x)	\lim\:_{x\to\:0}(\frac{x}{x^{2}-4x})
integral of 1/((ax+b)^2)	\int\:\frac{1}{(ax+b)^{2}}dx
limit as x approaches 3 of 1/(\|x-3\|)	\lim\:_{x\to\:3}(\frac{1}{\left\|x-3\right\|})
derivative of x^2*2x	\frac{d}{dx}(x^{2}\cdot\:2x)
derivative of x^2ln(x/2)	\frac{d}{dx}(x^{2}\ln(\frac{x}{2}))
limit as x approaches 2/3 of (3x-2)/(3x^2-11x+6)	\lim\:_{x\to\:\frac{2}{3}}(\frac{3x-2}{3x^{2}-11x+6})
(\partial)/(\partial z)(xy+yz+zx)	\frac{\partial\:}{\partial\:z}(xy+yz+zx)
derivative of xcos^3(x)	\frac{d}{dx}(x\cos^{3}(x))
integral from 1 to 2 of sqrt(x)ln(x)	\int\:_{1}^{2}\sqrt{x}\ln(x)dx
derivative of e^{(-3x})	\frac{d}{dx}(e^{(-3x)})
taylor e^{-3z+1}+8	taylor\:e^{-3z+1}+8
tangent of x^{2/3}+y^{2/3}=5,(1,8)	tangent\:x^{\frac{2}{3}}+y^{\frac{2}{3}}=5,(1,8)
derivative of f(x)=(2x-1)/(2x+1)	derivative\:f(x)=\frac{2x-1}{2x+1}
inverse oflaplace te^{-t}	inverselaplace\:te^{-t}
integral of (x+3)e^{x^2+6x}	\int\:(x+3)e^{x^{2}+6x}dx
limit as x approaches 1+of (x-1)/(\|x-1\|)	\lim\:_{x\to\:1+}(\frac{x-1}{\left\|x-1\right\|})
derivative of 2sec(x)tan(x)	derivative\:2\sec(x)\tan(x)
integral of cot^2(θ)csc(θ)	\int\:\cot^{2}(θ)\csc(θ)dθ
inverse oflaplace (s-1)/((s+1)(s^2+1))	inverselaplace\:\frac{s-1}{(s+1)(s^{2}+1)}
tangent of f(x)=(x-8)/(3x-4),\at x=2	tangent\:f(x)=\frac{x-8}{3x-4},\at\:x=2
derivative of cos(x{z}(x))	\frac{d}{dx}(\cos(x{z}(x)))
integral of x^{4/3}-3x^{5/2}	\int\:x^{\frac{4}{3}}-3x^{\frac{5}{2}}dx
integral of (x^3)/(x+1)	\int\:\frac{x^{3}}{x+1}dx
integral from 0 to 2 of 4-x^2	\int\:_{0}^{2}4-x^{2}dx
d/(dt)(1+2t)	\frac{d}{dt}(1+2t)
derivative of x^5-4x^3+2x-3	\frac{d}{dx}(x^{5}-4x^{3}+2x-3)
derivative of (x^2+xe^x)	\frac{d}{dx}((x^{2}+x)e^{x})
y^3dx=2x^3dy-2x^2ydx	y^{3}dx=2x^{3}dy-2x^{2}ydx
integral of sqrt(1+(16)/(9*x^{2/3))}	\int\:\sqrt{1+\frac{16}{9\cdot\:x^{\frac{2}{3}}}}dx
integral from 0 to 7 of sqrt(1+9x)	\int\:_{0}^{7}\sqrt{1+9x}dx
6y^{'''}+3y^{''}=0	6y^{\prime\:\prime\:\prime\:}+3y^{\prime\:\prime\:}=0
tangent of 3/((x+6)),\at x=-4	tangent\:\frac{3}{(x+6)},\at\:x=-4
y^'=7x+y	y^{\prime\:}=7x+y
(dy)/(dx)+3xy^2=0,y(0)=1	\frac{dy}{dx}+3xy^{2}=0,y(0)=1
derivative of ((6x^2/(4-x))^3)	\frac{d}{dx}((\frac{6x^{2}}{4-x})^{3})
sum from n=0 to infinity of n/(n^4+1)	\sum\:_{n=0}^{\infty\:}\frac{n}{n^{4}+1}
derivative of (x+9/(x^3+x-8))	\frac{d}{dx}(\frac{x+9}{x^{3}+x-8})
integral from-1 to 3 of x/(x^2+1)	\int\:_{-1}^{3}\frac{x}{x^{2}+1}dx
derivative of-6cos(t)	derivative\:-6\cos(t)
tangent of y=2x^3,(-2,-16)	tangent\:y=2x^{3},(-2,-16)
integral from 1 to-1 of (12x+11)^2	\int\:_{1}^{-1}(12x+11)^{2}dx
derivative of arcsin(xln(x))	\frac{d}{dx}(\arcsin(x\ln(x)))
integral from 0 to 1 of 5/(1+x^2)	\int\:_{0}^{1}\frac{5}{1+x^{2}}dx
(1+y/(x^2))dx-1/x dy=0	(1+\frac{y}{x^{2}})dx-\frac{1}{x}dy=0
(\partial)/(\partial x)((x^2)/(2y))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{2y})
derivative of-1/(4sin(x))	\frac{d}{dx}(-\frac{1}{4\sin(x)})
1/(-0.75y-0.00003)y^'=1	\frac{1}{-0.75y-0.00003}y^{\prime\:}=1
integral of x^3sqrt(x^2+5)	\int\:x^{3}\sqrt{x^{2}+5}dx
integral of (9-162x)/(sqrt(49-81x^2))	\int\:\frac{9-162x}{\sqrt{49-81x^{2}}}dx
derivative of 6\sqrt[3]{1-2x}	\frac{d}{dx}(6\sqrt[3]{1-2x})
limit as y approaches 5+of sqrt(y-5)	\lim\:_{y\to\:5+}(\sqrt{y-5})
limit as x approaches 3-of (3-x)/(x-3)	\lim\:_{x\to\:3-}(\frac{3-x}{x-3})
integral of (3x-1)^2(-2x)	\int\:(3x-1)^{2}(-2x)dx
slope of 7y^3+9x^8=5y+11x	slope\:7y^{3}+9x^{8}=5y+11x
f(x)=cot(2x)	f(x)=\cot(2x)
(\partial)/(\partial x)((3x)/(7y+5z))	\frac{\partial\:}{\partial\:x}(\frac{3x}{7y+5z})
integral of cos^4(3y)sin(3y)	\int\:\cos^{4}(3y)\sin(3y)dy
(\partial)/(\partial x)(2e^{7x})	\frac{\partial\:}{\partial\:x}(2e^{7x})
integral of 21z^3e^z	\int\:21z^{3}e^{z}dz
integral from 0 to 2 of y^3	\int\:_{0}^{2}y^{3}dy
(\partial)/(\partial x)(z/(y+z))	\frac{\partial\:}{\partial\:x}(\frac{z}{y+z})
sum from n=0 to infinity of (1-x)^n	\sum\:_{n=0}^{\infty\:}(1-x)^{n}
(\partial)/(\partial x)(ln(3x+6y+9t))	\frac{\partial\:}{\partial\:x}(\ln(3x+6y+9t))
tangent of f(x)= 1/(1+5x^2),\at x=-1	tangent\:f(x)=\frac{1}{1+5x^{2}},\at\:x=-1
d/(dt)(7t)	\frac{d}{dt}(7t)
(\partial)/(\partial x)(x/y-sin(y))	\frac{\partial\:}{\partial\:x}(\frac{x}{y}-\sin(y))
xy^{''}+2y^'=12x^2	xy^{\prime\:\prime\:}+2y^{\prime\:}=12x^{2}
integral from-1 to 1 of (4x)/((x+3)^2)	\int\:_{-1}^{1}\frac{4x}{(x+3)^{2}}dx
integral of (e^{4x})/4	\int\:\frac{e^{4x}}{4}dx
limit as x approaches infinity of n^x	\lim\:_{x\to\:\infty\:}(n^{x})
sum from n=1 to infinity of (n!)/(n^2)	\sum\:_{n=1}^{\infty\:}\frac{n!}{n^{2}}
integral from 0 to pi of sin^2(9x)	\int\:_{0}^{π}\sin^{2}(9x)dx
derivative of-2x*e^{-x^2}	\frac{d}{dx}(-2x\cdot\:e^{-x^{2}})

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