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Popular Calculus Problems

integral of (-7x^3)/(x^3+1)	\int\:\frac{-7x^{3}}{x^{3}+1}dx
derivative of 1/(e^{-x})	\frac{d}{dx}(\frac{1}{e^{-x}})
(\partial)/(\partial y)(2x^2e^{xy})	\frac{\partial\:}{\partial\:y}(2x^{2}e^{xy})
inverse oflaplace ((s-2)^2)/(s^3)	inverselaplace\:\frac{(s-2)^{2}}{s^{3}}
derivative of 2x^{1/2}+x^{-1}-2	\frac{d}{dx}(2x^{\frac{1}{2}}+x^{-1}-2)
integral of 1/(sqrt((x^2+4x+13)^3))	\int\:\frac{1}{\sqrt{(x^{2}+4x+13)^{3}}}dx
integral of (4sin(x)+(2x^5-sqrt(x))/x)	\int\:(4\sin(x)+\frac{2x^{5}-\sqrt{x}}{x})dx
derivative of f(x)=(4x^{3/2})/x	derivative\:f(x)=\frac{4x^{\frac{3}{2}}}{x}
derivative of (x^2+8x+3)/(sqrt(x))	derivative\:\frac{x^{2}+8x+3}{\sqrt{x}}
inverse oflaplace 3/5	inverselaplace\:\frac{3}{5}
derivative of cos(5x-9)	\frac{d}{dx}(\cos(5x-9))
inverse oflaplace (2s)/(s^2+s)	inverselaplace\:\frac{2s}{s^{2}+s}
derivative of y=3e^{4x}	derivative\:y=3e^{4x}
integral of 6x^2*e^{x^3}	\int\:6x^{2}\cdot\:e^{x^{3}}dx
integral of (x^2+x+1)/((x+1)^2(x+2))	\int\:\frac{x^{2}+x+1}{(x+1)^{2}(x+2)}dx
derivative of (xcos(x)(cos(x)+tan(x)))	\frac{d}{dx}((x\cos(x))(\cos(x)+\tan(x)))
integral from 0 to 1 of 1-x^{2/7}	\int\:_{0}^{1}1-x^{\frac{2}{7}}dx
x^2-3xy+xy^'=0	x^{2}-3xy+xy^{\prime\:}=0
d/(dt)(cos(t))	\frac{d}{dt}(\cos(t))
derivative of ln((5x+1/(5x-1)))	\frac{d}{dx}(\ln(\frac{5x+1}{5x-1}))
derivative of 15x^2+3	\frac{d}{dx}(15x^{2}+3)
y^{''}+4y^'+5y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=0,y(0)=1,y^{\prime\:}(0)=0
integral of 1/((1+y^2)arctan(y))	\int\:\frac{1}{(1+y^{2})\arctan(y)}dy
area y= 1/(14x^2),y=x,y= x/(12)	area\:y=\frac{1}{14x^{2}},y=x,y=\frac{x}{12}
sum from n=1 to infinity of n^2+1	\sum\:_{n=1}^{\infty\:}n^{2}+1
implicit 2xy-y^2=-1	implicit\:2xy-y^{2}=-1
derivative of cos^4(4x^2+1)	\frac{d}{dx}(\cos^{4}(4x^{2}+1))
integral of (3x^2+4x-6)	\int\:(3x^{2}+4x-6)dx
derivative of-1/3 (x^{-3}-x^6)	\frac{d}{dx}(-\frac{1}{3}(x^{-3}-x^{6}))
derivative of sqrt(33+4t)	derivative\:\sqrt{33+4t}
derivative of (x^2)/((4+x))	derivative\:\frac{x^{2}}{(4+x)}
integral of 1/(1+cos(θ))	\int\:\frac{1}{1+\cos(θ)}dθ
(\partial)/(\partial x)(3x^2cos^2(x-y))	\frac{\partial\:}{\partial\:x}(3x^{2}\cos^{2}(x-y))
(\partial)/(\partial x)(xcos(xy)-2y)	\frac{\partial\:}{\partial\:x}(x\cos(xy)-2y)
derivative of 3/(5-x)	\frac{d}{dx}(\frac{3}{5-x})
derivative of cos(xsec^7(x))	\frac{d}{dx}(\cos(x)\sec^{7}(x))
derivative of 2sin(x)+ce^{-x}cos(x)	derivative\:2\sin(x)+ce^{-x}\cos(x)
integral of 3sin^3(xco)s^2x	\int\:3\sin^{3}(xco)s^{2}xdx
derivative of-3x-4	\frac{d}{dx}(-3x-4)
derivative of 1728-1160x+34x^2+x^3	derivative\:1728-1160x+34x^{2}+x^{3}
integral of (5)	\int\:(5)dx
limit as x approaches 1 of (2x-5)/(x+1)	\lim\:_{x\to\:1}(\frac{2x-5}{x+1})
derivative of (kx+a/(bx+c))	\frac{d}{dx}(\frac{kx+a}{bx+c})
integral of ln(2x+1)	\int\:\ln(2x+1)dx
x((dy)/(dx))-y=2x^2	x(\frac{dy}{dx})-y=2x^{2}
integral of (e^x)/((6-e^x)^2)	\int\:\frac{e^{x}}{(6-e^{x})^{2}}dx
(\partial)/(\partial y)(x^2y^4)	\frac{\partial\:}{\partial\:y}(x^{2}y^{4})
limit as x approaches 2 of (x^2-2)/(x-2)	\lim\:_{x\to\:2}(\frac{x^{2}-2}{x-2})
sum from n=0 to infinity of 2+0.86^n	\sum\:_{n=0}^{\infty\:}2+0.86^{n}
integral of csc^3(2x)	\int\:\csc^{3}(2x)dx
limit as x approaches 0 of sin(5x)csc(9x)	\lim\:_{x\to\:0}(\sin(5x)\csc(9x))
inverse oflaplace ((s+1)^3)/(s^4)	inverselaplace\:\frac{(s+1)^{3}}{s^{4}}
derivative of y=(e^{x/2})/(x+1)	derivative\:y=\frac{e^{\frac{x}{2}}}{x+1}
derivative of 1/(x^6)	derivative\:\frac{1}{x^{6}}
integral from-infinity to 0 of xe^{3x}	\int\:_{-\infty\:}^{0}xe^{3x}dx
derivative of 2(x^3ln(x))	\frac{d}{dx}(2(x)^{3}\ln(x))
integral of xe^z+y^2	\int\:xe^{z}+y^{2}dz
derivative of ((x^2+3)/(x^2-3))^8	derivative\:(\frac{x^{2}+3}{x^{2}-3})^{8}
(dy)/(dx)=0.2(4000-y)	\frac{dy}{dx}=0.2(4000-y)
(\partial)/(\partial x)((xy)/(1+x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{xy}{1+x^{2}+y^{2}})
derivative of cos^2(2x-x^2)	\frac{d}{dx}(\cos^{2}(2x)-x^{2})
integral of \sqrt[3]{x+9}	\int\:\sqrt[3]{x+9}dx
(\partial)/(\partial x)(cos(3x+4y))	\frac{\partial\:}{\partial\:x}(\cos(3x+4y))
limit as x approaches 1 of 3-2x	\lim\:_{x\to\:1}(3-2x)
integral of sin(x)*sin(2x)	\int\:\sin(x)\cdot\:\sin(2x)dx
area y=x,y=-x+3,y=0	area\:y=x,y=-x+3,y=0
integral of (sin^2(2x))	\int\:(\sin^{2}(2x))dx
(dy)/(dx)=(y^3)/(3x-2)	\frac{dy}{dx}=\frac{y^{3}}{3x-2}
integral of 1/2 x+3	\int\:\frac{1}{2}x+3dx
limit as x approaches-6 of (2x+12)/(x+6)	\lim\:_{x\to\:-6}(\frac{2x+12}{x+6})
limit as x approaches 0 of (10)/(x(x+1))	\lim\:_{x\to\:0}(\frac{10}{x(x+1)})
derivative of y=e^{-2x}	derivative\:y=e^{-2x}
derivative of x+cot(x)	\frac{d}{dx}(x+\cot(x))
tangent of f(x)=x^2+x,(4,20)	tangent\:f(x)=x^{2}+x,(4,20)
integral from 0 to 7 of (x+1)^2	\int\:_{0}^{7}(x+1)^{2}dx
(\partial)/(\partial x)(z/(sqrt(x+y^2)))	\frac{\partial\:}{\partial\:x}(\frac{z}{\sqrt{x+y^{2}}})
integral from-pi to pi of sin(x)	\int\:_{-π}^{π}\sin(x)dx
limit as x approaches-1-of 2x^2-4x+2	\lim\:_{x\to\:-1-}(2x^{2}-4x+2)
tangent of f(x)=4x^2-3x-7,\at x=2	tangent\:f(x)=4x^{2}-3x-7,\at\:x=2
inverse oflaplace (2s)/((s^2+4s+13))	inverselaplace\:\frac{2s}{(s^{2}+4s+13)}
limit as x approaches 0 of sin(x) 1/x	\lim\:_{x\to\:0}(\sin(x)\frac{1}{x})
integral from 1 to 2 of (15)/(x^3+2x)	\int\:_{1}^{2}\frac{15}{x^{3}+2x}dx
derivative of 2xln(sqrt(x)+1)	\frac{d}{dx}(2x\ln(\sqrt{x}+1))
integral of ((ln(z))^5)/z	\int\:\frac{(\ln(z))^{5}}{z}dz
integral of e^{-12x}	\int\:e^{-12x}dx
limit as x approaches 5 of (7x)/(x-5)	\lim\:_{x\to\:5}(\frac{7x}{x-5})
y^'+y=e^{2x}	y^{\prime\:}+y=e^{2x}
derivative of sqrt(x)+5/(sqrt(x))	derivative\:\sqrt{x}+\frac{5}{\sqrt{x}}
integral of (x^2-1)^2(3x^2)	\int\:(x^{2}-1)^{2}(3x^{2})dx
(dx)/(dy)=e^{3x+2y}	\frac{dx}{dy}=e^{3x+2y}
derivative of x/(x+16)	\frac{d}{dx}(\frac{x}{x+16})
limit as x approaches 3 of 0/(x-3)	\lim\:_{x\to\:3}(\frac{0}{x-3})
sum from n=0 to infinity of 11^n	\sum\:_{n=0}^{\infty\:}11^{n}
derivative of ln(x^3+x)	\frac{d}{dx}(\ln(x^{3}+x))
integral of e^{(-x+2)/3}	\int\:e^{\frac{-x+2}{3}}dx
y^{''}-16y=(16x)/(e^{4x)}	y^{\prime\:\prime\:}-16y=\frac{16x}{e^{4x}}
integral from 0 to infinity of 2xe^{-x}	\int\:_{0}^{\infty\:}2xe^{-x}dx
integral of e^{-1/2 x^2}	\int\:e^{-\frac{1}{2}x^{2}}dx
y^{''}+2y+y=2e^{-t}	y^{\prime\:\prime\:}+2y+y=2e^{-t}
derivative of x/(sqrt(x-2))	derivative\:\frac{x}{\sqrt{x-2}}

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