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Popular Calculus Problems

maclaurin (1-x^2)^{1/2}	maclaurin\:(1-x^{2})^{\frac{1}{2}}
2sqrt(xy)(dy)/(dx)=3	2\sqrt{xy}\frac{dy}{dx}=3
integral of (ln(x)-1)/x	\int\:\frac{\ln(x)-1}{x}dx
limit as x approaches 1 of 3x-6	\lim\:_{x\to\:1}(3x-6)
derivative of ln(\sqrt[6]{(x-5/(x+5)}))	\frac{d}{dx}(\ln(\sqrt[6]{\frac{x-5}{x+5}}))
inverse oflaplace (2se^{-2s})/(5s^2+45)	inverselaplace\:\frac{2se^{-2s}}{5s^{2}+45}
(dy)/(dx)= y/((1+x^2))	\frac{dy}{dx}=\frac{y}{(1+x^{2})}
y^{''}-y^'-2y=4e^{-t}	y^{\prime\:\prime\:}-y^{\prime\:}-2y=4e^{-t}
derivative of f(x)= 2/(x-7)	derivative\:f(x)=\frac{2}{x-7}
integral of 8xe^{-x^2}	\int\:8xe^{-x^{2}}dx
limit as x approaches 2 of (x+3)/(x-2)	\lim\:_{x\to\:2}(\frac{x+3}{x-2})
derivative of-2/(3x^3)	\frac{d}{dx}(-\frac{2}{3x^{3}})
integral of (18)/((x-3)(x^2+9))	\int\:\frac{18}{(x-3)(x^{2}+9)}dx
integral of 2/7 sec(x)tan(x)	\int\:\frac{2}{7}\sec(x)\tan(x)dx
(dy)/(dt)=(6t^5)/(1+t^6)y+7(1+t^6)^2	\frac{dy}{dt}=\frac{6t^{5}}{1+t^{6}}y+7(1+t^{6})^{2}
laplacetransform t^{10}	laplacetransform\:t^{10}
derivative of sin^3(xco)s^5x	derivative\:\sin^{3}(xco)s^{5}x
integral of 5arctan(1/x)	\int\:5\arctan(\frac{1}{x})dx
integral of x^2ln\|x\|	\int\:x^{2}\ln\left\|x\right\|dx
limit as x approaches 1 of x(x-1)ln(x+1)	\lim\:_{x\to\:1}(x(x-1)\ln(x+1))
integral of (2x^2)^2	\int\:(2x^{2})^{2}dx
laplacetransform 1/2 e^t-1/2 cos(t)-1/2 sin(t)	laplacetransform\:\frac{1}{2}e^{t}-\frac{1}{2}\cos(t)-\frac{1}{2}\sin(t)
laplacetransform 2e^{2t}	laplacetransform\:2e^{2t}
area y=x-2,x=y^2	area\:y=x-2,x=y^{2}
integral from-1 to 1 of (1-x^2)^{3/2}	\int\:_{-1}^{1}(1-x^{2})^{\frac{3}{2}}dx
tangent of (sqrt(x))/(6x-4),\at x=9	tangent\:\frac{\sqrt{x}}{6x-4},\at\:x=9
(\partial)/(\partial x)(2x^4yz^3)	\frac{\partial\:}{\partial\:x}(2x^{4}yz^{3})
integral of 1/(\sqrt[3]{x)+\sqrt[4]{x}}	\int\:\frac{1}{\sqrt[3]{x}+\sqrt[4]{x}}dx
limit as x approaches 0-of 6/(5x^{1/3)}	\lim\:_{x\to\:0-}(\frac{6}{5x^{\frac{1}{3}}})
integral of (5x^2-2x+3)	\int\:(5x^{2}-2x+3)dx
derivative of-8/(\sqrt[4]{x)}	derivative\:-\frac{8}{\sqrt[4]{x}}
limit as x approaches infinity of 5x+1/x	\lim\:_{x\to\:\infty\:}(5x+\frac{1}{x})
(\partial)/(\partial x)(t^2+4x^3)	\frac{\partial\:}{\partial\:x}(t^{2}+4x^{3})
integral of-1/3 cos(3x)	\int\:-\frac{1}{3}\cos(3x)dx
integral of (2x^2)/(3-4x^3)	\int\:\frac{2x^{2}}{3-4x^{3}}dx
derivative of-2	derivative\:-2
derivative of arctan(xy)	\frac{d}{dx}(\arctan(xy))
integral of ((3x-2))/(5x^2-3x+2)	\int\:\frac{(3x-2)}{5x^{2}-3x+2}dx
derivative of f(x)= 3/(1+x^2)	derivative\:f(x)=\frac{3}{1+x^{2}}
integral from 0 to 1 of 3x^2(x^3+5)^{-2}	\int\:_{0}^{1}3x^{2}(x^{3}+5)^{-2}dx
integral of sin(5pi)t	\int\:\sin(5π)tdt
2y^{''}-8y=0	2y^{\prime\:\prime\:}-8y=0
derivative of-e^x(x-7)	\frac{d}{dx}(-e^{x}(x-7))
(\partial)/(\partial y)(-10ysin(xy))	\frac{\partial\:}{\partial\:y}(-10y\sin(xy))
derivative of y=x^{x^2}	derivative\:y=x^{x^{2}}
(\partial)/(\partial x)(-xcos(y))	\frac{\partial\:}{\partial\:x}(-x\cos(y))
integral of 3cos(x)-1/(sqrt(x))	\int\:3\cos(x)-\frac{1}{\sqrt{x}}dx
integral from 1 to 11 of 1/(x-8)	\int\:_{1}^{11}\frac{1}{x-8}dx
integral from-2 to 2 of (10)/(x^2-4x-21)	\int\:_{-2}^{2}\frac{10}{x^{2}-4x-21}dx
integral of (3sec(x)tan(x)-5csc^2(x))	\int\:(3\sec(x)\tan(x)-5\csc^{2}(x))dx
derivative of acos(wx)	\frac{d}{dx}(a\cos(wx))
integral of 4^u	\int\:4^{u}du
sum from n=1 to infinity of 2/(2^n)	\sum\:_{n=1}^{\infty\:}\frac{2}{2^{n}}
integral of x(sin^2(x))	\int\:x(\sin^{2}(x))dx
2y^{''}+16y^'+32y=0,y(0)=-3,y^'(0)=10	2y^{\prime\:\prime\:}+16y^{\prime\:}+32y=0,y(0)=-3,y^{\prime\:}(0)=10
derivative of {f}(x(x)^3(x))	\frac{d}{dx}({f}(x)(x)^{3}(x))
tangent of f(x)=cos(2x)	tangent\:f(x)=\cos(2x)
integral of 1/((2x+1)^2)	\int\:\frac{1}{(2x+1)^{2}}dx
integral of sec^5(x)tan^3(x)	\int\:\sec^{5}(x)\tan^{3}(x)dx
limit as x approaches 0 of ((x+1)^5-1)/x	\lim\:_{x\to\:0}(\frac{(x+1)^{5}-1}{x})
integral of A*e^{t(1+sqrt(3))}	\int\:A\cdot\:e^{t(1+\sqrt{3})}dt
integral of 1/((u-1)^2)	\int\:\frac{1}{(u-1)^{2}}du
integral of-8xsin(4x^2+1)	\int\:-8x\sin(4x^{2}+1)dx
x^2+5y(dy)/(dx)=0	x^{2}+5y\frac{dy}{dx}=0
limit as x approaches-1 of (9x+1)^2	\lim\:_{x\to\:-1}((9x+1)^{2})
integral of 2xye^{x^2}	\int\:2xye^{x^{2}}dx
integral of 1/(x(ln(x^4))^6)	\int\:\frac{1}{x(\ln(x^{4}))^{6}}dx
limit as x approaches 0 of (sin(4x))/9	\lim\:_{x\to\:0}(\frac{\sin(4x)}{9})
derivative of 1/(sqrt(2x+5))	\frac{d}{dx}(\frac{1}{\sqrt{2x+5}})
inverse oflaplace 6/(s^2(s+2))	inverselaplace\:\frac{6}{s^{2}(s+2)}
(\partial)/(\partial y)(xe^{x+y}-y)	\frac{\partial\:}{\partial\:y}(xe^{x+y}-y)
derivative of 4sin(x/2)	\frac{d}{dx}(4\sin(\frac{x}{2}))
integral from-infinity to 0 of 1/(7-9x)	\int\:_{-\infty\:}^{0}\frac{1}{7-9x}dx
derivative of 5e^{-2x}+4	\frac{d}{dx}(5e^{-2x}+4)
derivative of 8^{4-x^2}	\frac{d}{dx}(8^{4-x^{2}})
slope of (x^2-35)^6	slope\:(x^{2}-35)^{6}
derivative of 1/(sin(x+cos(x)))	\frac{d}{dx}(\frac{1}{\sin(x)+\cos(x)})
area y=x^2+2,y=-x,x=0,x=1	area\:y=x^{2}+2,y=-x,x=0,x=1
integral of (29)/((x+1)(x^2+x))	\int\:\frac{29}{(x+1)(x^{2}+x)}dx
derivative of y=(e^x)/(9x^2)	derivative\:y=\frac{e^{x}}{9x^{2}}
integral of ((x^2))/(sqrt(13-4x+x^2))	\int\:\frac{(x^{2})}{\sqrt{13-4x+x^{2}}}dx
derivative of (x+6/(x^3+x-1))	\frac{d}{dx}(\frac{x+6}{x^{3}+x-1})
y^{''}+4y^'+3y=te^{-t}	y^{\prime\:\prime\:}+4y^{\prime\:}+3y=te^{-t}
limit as x approaches 6 of (3x)/(x-6)	\lim\:_{x\to\:6}(\frac{3x}{x-6})
integral of r^2e^r	\int\:r^{2}e^{r}dr
derivative of cos(arctan(x))	\frac{d}{dx}(\cos(\arctan(x)))
integral of 6e^{2x}	\int\:6e^{2x}dx
derivative of 4cos(t)-9sin(t)	derivative\:4\cos(t)-9\sin(t)
(\partial)/(\partial x)(x^9yz^2+5yz)	\frac{\partial\:}{\partial\:x}(x^{9}yz^{2}+5yz)
integral of cos^3(2x)sin^3(2x)	\int\:\cos^{3}(2x)\sin^{3}(2x)dx
cos(y)y^'=e^{2x}+1	\cos(y)y^{\prime\:}=e^{2x}+1
derivative of (y^3)/(30)+5/(2y)	derivative\:\frac{y^{3}}{30}+\frac{5}{2y}
derivative of ln(1+x)	derivative\:\ln(1+x)
integral of sqrt(1+cos(t))	\int\:\sqrt{1+\cos(t)}dt
inverse oflaplace 1/(s^2+12s+100)	inverselaplace\:\frac{1}{s^{2}+12s+100}
integral from 0 to 1 of sqrt(1+12x)	\int\:_{0}^{1}\sqrt{1+12x}dx
limit as x approaches 7 of sqrt(3)	\lim\:_{x\to\:7}(\sqrt{3})
integral of (4x+2)e^{2x}	\int\:(4x+2)e^{2x}dx
limit as x approaches 0 of ln(6x+1)	\lim\:_{x\to\:0}(\ln(6x+1))
integral of (x^3+16)/(x^2+16)	\int\:\frac{x^{3}+16}{x^{2}+16}dx

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