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Popular Calculus Problems

derivative of xlog_{10}(2/x)	\frac{d}{dx}(x\log_{10}(\frac{2}{x}))
integral of (x^2-1)/x	\int\:\frac{x^{2}-1}{x}dx
integral of (-x+1)/(x^2+1)	\int\:\frac{-x+1}{x^{2}+1}dx
maclaurin (1/3)^x	maclaurin\:(\frac{1}{3})^{x}
integral from 0 to 1 of sqrt(2x+1)	\int\:_{0}^{1}\sqrt{2x+1}dx
limit as x approaches infinity+of sqrt(25x^4+9x)-5x^2	\lim\:_{x\to\:\infty\:+}(\sqrt{25x^{4}+9x}-5x^{2})
derivative of 2^e	\frac{d}{dx}(2^{e})
integral of (e^x)/2+xsqrt(x)	\int\:\frac{e^{x}}{2}+x\sqrt{x}dx
tangent of f(x)=-3cos(x),\at x=-pi/3	tangent\:f(x)=-3\cos(x),\at\:x=-\frac{π}{3}
integral of (1-1/(x^2))sqrt(x\sqrt{x)}	\int\:(1-\frac{1}{x^{2}})\sqrt{x\sqrt{x}}dx
derivative of 3x^2-y^2	\frac{d}{dx}(3x^{2}-y^{2})
integral of sec(t)sec(t)+tan(t)	\int\:\sec(t)\sec(t)+\tan(t)dt
integral from 0 to infinity of e^{-\|x\|}	\int\:_{0}^{\infty\:}e^{-\left\|x\right\|}dx
derivative of (3x^2-9^{-12})	\frac{d}{dx}((3x^{2}-9)^{-12})
slope of y=2^x	slope\:y=2^{x}
integral of \sqrt[3]{3x-4}	\int\:\sqrt[3]{3x-4}dx
integral of 5sin^3(3x)cos^3(3x)	\int\:5\sin^{3}(3x)\cos^{3}(3x)dx
area y= 4/3 ,y= 1/(sqrt(9-x^2))	area\:y=\frac{4}{3},y=\frac{1}{\sqrt{9-x^{2}}}
integral from-1 to 1/2 of 1/4 (3x^2+1)	\int\:_{-1}^{\frac{1}{2}}\frac{1}{4}(3x^{2}+1)dx
y^'=1-x+4y	y^{\prime\:}=1-x+4y
(\partial)/(\partial x)(5e^{x^6y})	\frac{\partial\:}{\partial\:x}(5e^{x^{6}y})
simplify (3x+6)/(2sqrt(x+3))	simplify\:\frac{3x+6}{2\sqrt{x+3}}
integral from-4 to 2 of-(y^2)/2-y+4	\int\:_{-4}^{2}-\frac{y^{2}}{2}-y+4dy
derivative of f(x)=(x^5)/7	derivative\:f(x)=\frac{x^{5}}{7}
integral of sqrt(cos(2x-2))	\int\:\sqrt{\cos(2x-2)}dx
integral of (x^4)/(9-x^5)	\int\:\frac{x^{4}}{9-x^{5}}dx
y^'=e^{-x}y	y^{\prime\:}=e^{-x}y
y^{''}-3y^'-10y=-3x^2e^{-6x}	y^{\prime\:\prime\:}-3y^{\prime\:}-10y=-3x^{2}e^{-6x}
sum from n=0 to infinity of (-2/5)^n	\sum\:_{n=0}^{\infty\:}(-\frac{2}{5})^{n}
inverse oflaplace 8/(s^3)	inverselaplace\:\frac{8}{s^{3}}
derivative of-4/(sqrt(x))	\frac{d}{dx}(-\frac{4}{\sqrt{x}})
limit as x approaches pi/2 of 2tan(x)	\lim\:_{x\to\:\frac{π}{2}}(2\tan(x))
integral of (8-128x)/(sqrt(25-64x^2))	\int\:\frac{8-128x}{\sqrt{25-64x^{2}}}dx
f(x)=x^{-6}	f(x)=x^{-6}
integral of 1/(x^2+8x+17)	\int\:\frac{1}{x^{2}+8x+17}dx
(d^4)/(dx^4)(e^{-x^2})	\frac{d^{4}}{dx^{4}}(e^{-x^{2}})
derivative of 3/(4x+2)+3x^2	derivative\:\frac{3}{4x+2}+3x^{2}
derivative of e^{-x}x^2	\frac{d}{dx}(e^{-x}x^{2})
limit as x approaches-2-of (x+5)/(x+4)	\lim\:_{x\to\:-2-}(\frac{x+5}{x+4})
derivative of (x^2-9^{2/3})	\frac{d}{dx}((x^{2}-9)^{\frac{2}{3}})
integral of (3x^2+2x-3)	\int\:(3x^{2}+2x-3)dx
sum from n=1 to infinity of 9/((n+1)!)	\sum\:_{n=1}^{\infty\:}\frac{9}{(n+1)!}
tangent of f(x)=8x^2,\at x=10	tangent\:f(x)=8x^{2},\at\:x=10
integral of (sqrt(5-x^2))/(x^2)	\int\:\frac{\sqrt{5-x^{2}}}{x^{2}}dx
integral of 1+tan^2(x)-2cos(x)	\int\:1+\tan^{2}(x)-2\cos(x)dx
(\partial)/(\partial r)(pi/3 h^2(3r-h))	\frac{\partial\:}{\partial\:r}(\frac{π}{3}h^{2}(3r-h))
e^xydy=(e^{-y}+e^{2x-y})dx	e^{x}ydy=(e^{-y}+e^{2x-y})dx
sum from n=1 to infinity of ne^{5n}	\sum\:_{n=1}^{\infty\:}ne^{5n}
integral from 0 to 2 of 10000e^{0.04x}	\int\:_{0}^{2}10000e^{0.04x}dx
integral of (5x^2+6x+9)/((x-3)^2(x+1)^2)	\int\:\frac{5x^{2}+6x+9}{(x-3)^{2}(x+1)^{2}}dx
derivative of (x^6/(sqrt(1+x^{12))})	\frac{d}{dx}(\frac{x^{6}}{\sqrt{1+x^{12}}})
integral of ((sqrt(x)+3)^2)/(sqrt(x))	\int\:\frac{(\sqrt{x}+3)^{2}}{\sqrt{x}}dx
(\partial)/(\partial y)(x^2+y^2-25)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}-25)
integral of-0.04t	\int\:-0.04tdt
derivative of-2/9 x^{-5/3}	\frac{d}{dx}(-\frac{2}{9}x^{-\frac{5}{3}})
derivative of f(x)=(699)/((x+1)^{0.94)}	derivative\:f(x)=\frac{699}{(x+1)^{0.94}}
integral from-1/2 to 0 of x^4*e^{2x+1}	\int\:_{-\frac{1}{2}}^{0}x^{4}\cdot\:e^{2x+1}dx
limit as x approaches infinity of x/c	\lim\:_{x\to\:\infty\:}(\frac{x}{c})
integral of e^{nx}	\int\:e^{nx}dx
derivative of x^4-8x^2-4	\frac{d}{dx}(x^{4}-8x^{2}-4)
integral of (sqrt(x)+2)/(\sqrt[3]{x)}	\int\:\frac{\sqrt{x}+2}{\sqrt[3]{x}}dx
integral of (x-4)/((x+4)(x+3)^2)	\int\:\frac{x-4}{(x+4)(x+3)^{2}}dx
derivative of 1/5 x^5-1/(2x^4+3x+9)	\frac{d}{dx}(\frac{1}{5}x^{5}-\frac{1}{2x^{4}}+3x+9)
y^{''}+5y^'-14y=0	y^{\prime\:\prime\:}+5y^{\prime\:}-14y=0
derivative of (sqrt(x)/(2e^x))	\frac{d}{dx}(\frac{\sqrt{x}}{2e^{x}})
(\partial)/(\partial x)(15x^2-25xy+9y^2)	\frac{\partial\:}{\partial\:x}(15x^{2}-25xy+9y^{2})
limit as x approaches 8 of 5x+\|x-8\|	\lim\:_{x\to\:8}(5x+\left\|x-8\right\|)
(\partial)/(\partial x)(2ln(x)+ln(y))	\frac{\partial\:}{\partial\:x}(2\ln(x)+\ln(y))
tangent of f(x)=sqrt(x-3),(12,3)	tangent\:f(x)=\sqrt{x-3},(12,3)
integral from 1 to 4 of 1	\int\:_{1}^{4}1
limit as x approaches 21 of x	\lim\:_{x\to\:21}(x)
integral from-1 to 2 of (x^2)/8	\int\:_{-1}^{2}\frac{x^{2}}{8}dx
laplacetransform (et^4)/(24)	laplacetransform\:\frac{et^{4}}{24}
(dx)/(dt)+xe^t=1-x	\frac{dx}{dt}+xe^{t}=1-x
slope of (5,-6),(8,-4)	slope\:(5,-6),(8,-4)
limit as x approaches 0 of 1-3x	\lim\:_{x\to\:0}(1-3x)
xy^'+1/2 y=x	xy^{\prime\:}+\frac{1}{2}y=x
(\partial)/(\partial x)(ln(x^4y))	\frac{\partial\:}{\partial\:x}(\ln(x^{4}y))
derivative of xsinh(x-6cosh(x))	\frac{d}{dx}(x\sinh(x)-6\cosh(x))
(dy)/(dx)=2y^2+3	\frac{dy}{dx}=2y^{2}+3
(\partial)/(\partial x)((x/y)^2)	\frac{\partial\:}{\partial\:x}((\frac{x}{y})^{2})
integral of (x^2)/(2+x)	\int\:\frac{x^{2}}{2+x}dx
integral of (x^2)/(sqrt(x+3))	\int\:\frac{x^{2}}{\sqrt{x+3}}dx
integral of (sqrt(a^2-x^2))/(x^2)	\int\:\frac{\sqrt{a^{2}-x^{2}}}{x^{2}}dx
area y=11x,y=x^2-12	area\:y=11x,y=x^{2}-12
integral from 1 to 4 of (x^2)	\int\:_{1}^{4}(x^{2})dx
integral from 1 to 3 of sqrt(1+1/(x^2))	\int\:_{1}^{3}\sqrt{1+\frac{1}{x^{2}}}dx
sum from n=0 to infinity of 0.4^n	\sum\:_{n=0}^{\infty\:}0.4^{n}
derivative of e^{-x^2+7x}	\frac{d}{dx}(e^{-x^{2}+7x})
y^{''}+1.875y^'+0.125y=0,y(0)=2,y^'(0)=1	y^{\prime\:\prime\:}+1.875y^{\prime\:}+0.125y=0,y(0)=2,y^{\prime\:}(0)=1
derivative of 4pi	\frac{d}{dx}(4π)
limit as h approaches 0 of (sin(7h))/h	\lim\:_{h\to\:0}(\frac{\sin(7h)}{h})
integral from 0 to 4 of x-2	\int\:_{0}^{4}x-2dx
integral from 0 to 24 of xe^{-x}	\int\:_{0}^{24}xe^{-x}dx
integral of x+1/(x^3)	\int\:x+\frac{1}{x^{3}}dx
inverse oflaplace s/(2s^2+2s+1)	inverselaplace\:\frac{s}{2s^{2}+2s+1}
integral from 1 to 2 of 4^{-x}	\int\:_{1}^{2}4^{-x}dx
y^'+2y=2t	y^{\prime\:}+2y=2t
integral of 2x+7e^x	\int\:2x+7e^{x}dx
limit as x approaches 2 of x	\lim\:_{x\to\:2}(x)

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