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Popular Calculus Problems

inverse oflaplace (16)/((s-1)(s+1))	inverselaplace\:\frac{16}{(s-1)(s+1)}
inverse oflaplace 2/(s^2(s^2+25))	inverselaplace\:\frac{2}{s^{2}(s^{2}+25)}
(\partial)/(\partial x)(4ysin(2x))	\frac{\partial\:}{\partial\:x}(4y\sin(2x))
e^yy^'=e^y+7x	e^{y}y^{\prime\:}=e^{y}+7x
integral of xsin(2x^2)	\int\:x\sin(2x^{2})dx
derivative of 5x^7sin(x)	\frac{d}{dx}(5x^{7}\sin(x))
derivative of f(x)=(cot(x))/(sin(x))	derivative\:f(x)=\frac{\cot(x)}{\sin(x)}
derivative of ln(sqrt(x+1))	derivative\:\ln(\sqrt{x+1})
(dy)/(dt)=0.3y+26e^{0.3t}	\frac{dy}{dt}=0.3y+26e^{0.3t}
derivative of (8x^2+4x+8)/(sqrt(x))	derivative\:\frac{8x^{2}+4x+8}{\sqrt{x}}
(\partial)/(\partial x)(x^{sqrt(2)})	\frac{\partial\:}{\partial\:x}(x^{\sqrt{2}})
derivative of f(x)=6ln(sec(x)+tan(x))	derivative\:f(x)=6\ln(\sec(x)+\tan(x))
integral of p(p+5)^7	\int\:p(p+5)^{7}dp
integral of x/(x^2+6x+10)	\int\:\frac{x}{x^{2}+6x+10}dx
derivative of (6x^2+6x+8/(sqrt(x)))	\frac{d}{dx}(\frac{6x^{2}+6x+8}{\sqrt{x}})
y^'+6(tan(6x))y=-cos(6x)	y^{\prime\:}+6(\tan(6x))y=-\cos(6x)
integral of 2^x(1+5^x)	\int\:2^{x}(1+5^{x})dx
(dy)/(dt)=y^{1/3},y(0)=0	\frac{dy}{dt}=y^{\frac{1}{3}},y(0)=0
integral of (ln(x))^3	\int\:(\ln(x))^{3}dx
tangent of f(x)=x^2+3x-1,\at x=1	tangent\:f(x)=x^{2}+3x-1,\at\:x=1
y^{''}-4=0	y^{\prime\:\prime\:}-4=0
derivative of (2x+3(3x-2))	\frac{d}{dx}((2x+3)(3x-2))
6y^'-y=9x^{-3x},y(0)=4	6y^{\prime\:}-y=9x^{-3x},y(0)=4
taylor (2x+4)/(3x+7),\at-2	taylor\:\frac{2x+4}{3x+7},\at\:-2
derivative of (sin(xy)/(e^x-y^2))	\frac{d}{dx}(\frac{\sin(xy)}{e^{x}-y^{2}})
derivative of 2xy^2	derivative\:2xy^{2}
sum from n=0 to infinity of n*(2/3)^n	\sum\:_{n=0}^{\infty\:}n\cdot\:(\frac{2}{3})^{n}
derivative of 4e^{2x^2-4}	derivative\:4e^{2x^{2}-4}
tangent of-3/2 x^2+9x+9	tangent\:-\frac{3}{2}x^{2}+9x+9
integral of (12x^3-4x-2)	\int\:(12x^{3}-4x-2)dx
integral of 1/(1/v)	\int\:\frac{1}{\frac{1}{v}}dv
inverse oflaplace (e^{-2s})/(s^2+1)	inverselaplace\:\frac{e^{-2s}}{s^{2}+1}
implicit 5x^2+y^2=9	implicit\:5x^{2}+y^{2}=9
integral of x^3sqrt(x+1)	\int\:x^{3}\sqrt{x+1}dx
y^{''}-2y^'-24y=0	y^{\prime\:\prime\:}-2y^{\prime\:}-24y=0
integral of x^3(x^4+3)^3	\int\:x^{3}(x^{4}+3)^{3}dx
integral of 4^{(8-2x)}	\int\:4^{(8-2x)}dx
integral of ((4x^4-6x^2)/x)	\int\:(\frac{4x^{4}-6x^{2}}{x})dx
derivative of y=6e^x+8/(\sqrt[3]{x)}	derivative\:y=6e^{x}+\frac{8}{\sqrt[3]{x}}
integral of (x^2ln(2x))	\int\:(x^{2}\ln(2x))dx
taylor e^{x^2}-1	taylor\:e^{x^{2}}-1
integral of (x/2)^4	\int\:(\frac{x}{2})^{4}dx
y^'= y/x	y^{\prime\:}=\frac{y}{x}
(\partial)/(\partial y)(1/(ln(10)(x-y)))	\frac{\partial\:}{\partial\:y}(\frac{1}{\ln(10)(x-y)})
(dy)/(dt)+3y+e^t+3=0	\frac{dy}{dt}+3y+e^{t}+3=0
dx-x^2dy=0	dx-x^{2}dy=0
derivative of 2/(1-8x)	derivative\:\frac{2}{1-8x}
integral of e^{-sx}*sin(x)	\int\:e^{-sx}\cdot\:\sin(x)dx
integral of (6sec^2(x))	\int\:(6\sec^{2}(x))dx
limit as x approaches 0+of 9/x-9/(\|x\|)	\lim\:_{x\to\:0+}(\frac{9}{x}-\frac{9}{\left\|x\right\|})
limit as x approaches-2 of 3-x	\lim\:_{x\to\:-2}(3-x)
sum from n=0 to infinity of (10^n)/(9^n)	\sum\:_{n=0}^{\infty\:}\frac{10^{n}}{9^{n}}
x^3+3y-x(dy)/(dx)=0	x^{3}+3y-x\frac{dy}{dx}=0
y^{''}+36y=2tan(6x)	y^{\prime\:\prime\:}+36y=2\tan(6x)
derivative of e^{arctan(x})	\frac{d}{dx}(e^{\arctan(x)})
(\partial)/(\partial x)(4x^3-3x^2y+5x)	\frac{\partial\:}{\partial\:x}(4x^{3}-3x^{2}y+5x)
derivative of sqrt(x)-1	derivative\:\sqrt{x}-1
integral of 1/(x(y+1))	\int\:\frac{1}{x(y+1)}dy
integral of 4tan(x)sec^3(x)	\int\:4\tan(x)\sec^{3}(x)dx
taylor 9+x*e^{-7x}	taylor\:9+x\cdot\:e^{-7x}
limit as x approaches 10 of (x^2-99)/(x-10)	\lim\:_{x\to\:10}(\frac{x^{2}-99}{x-10})
integral of (2x^5-3x^4+4x^2)	\int\:(2x^{5}-3x^{4}+4x^{2})dx
integral of (sec(x))/(cos(x))	\int\:\frac{\sec(x)}{\cos(x)}dx
(\partial)/(\partial x)(49-7x^2-y^2)	\frac{\partial\:}{\partial\:x}(49-7x^{2}-y^{2})
integral of (x^3)/((1+x^4)^{1/3)}	\int\:\frac{x^{3}}{(1+x^{4})^{\frac{1}{3}}}dx
integral of 12x+4y	\int\:12x+4ydy
limit as x approaches 2 of asqrt(x+7)+b	\lim\:_{x\to\:2}(a\sqrt{x+7}+b)
(\partial)/(\partial x)(ln(y+2))	\frac{\partial\:}{\partial\:x}(\ln(y+2))
(e^{x^3})^'	(e^{x^{3}})^{\prime\:}
integral of 4xcos(x^2)	\int\:4x\cos(x^{2})dx
(\partial)/(\partial t)(-2/t)	\frac{\partial\:}{\partial\:t}(-\frac{2}{t})
integral of (x+6)/(x^2+4)	\int\:\frac{x+6}{x^{2}+4}dx
integral of 8xcos(4x^2+3)	\int\:8x\cos(4x^{2}+3)dx
derivative of 1/3 e^x	\frac{d}{dx}(\frac{1}{3}e^{x})
limit as h approaches 0 of (cosh(x))/h	\lim\:_{h\to\:0}(\frac{\cosh(x)}{h})
integral of 9/(x^2+16)	\int\:\frac{9}{x^{2}+16}dx
integral of (1-tan^2(x))/(sec^2(x))	\int\:\frac{1-\tan^{2}(x)}{\sec^{2}(x)}dx
derivative of (x^2)/(3+sqrt(x))	derivative\:\frac{x^{2}}{3+\sqrt{x}}
taylor ln(1+x),3	taylor\:\ln(1+x),3
integral of 3/(x^2)+2/(x^3)	\int\:\frac{3}{x^{2}}+\frac{2}{x^{3}}dx
x(dy)/(dx)=y(ln(y)-ln(x))	x\frac{dy}{dx}=y(\ln(y)-\ln(x))
derivative of (ln(x-1)/(ln^2(x)))	\frac{d}{dx}(\frac{\ln(x)-1}{\ln^{2}(x)})
area (12)/(1+x^4),6x^2	area\:\frac{12}{1+x^{4}},6x^{2}
derivative of 2x^x	derivative\:2x^{x}
sum from n=0 to infinity of (2^2)/(3^2)	\sum\:_{n=0}^{\infty\:}\frac{2^{2}}{3^{2}}
(\partial)/(\partial s)(-3s^2t^2)	\frac{\partial\:}{\partial\:s}(-3s^{2}t^{2})
(dy)/(dx)=(y^3)/(3x+1),y(0)=-1	\frac{dy}{dx}=\frac{y^{3}}{3x+1},y(0)=-1
derivative of 2/(t^3)	derivative\:\frac{2}{t^{3}}
y^'+3y=xe^{-2x}	y^{\prime\:}+3y=xe^{-2x}
(\partial)/(\partial y)(-sin(x)sin(y))	\frac{\partial\:}{\partial\:y}(-\sin(x)\sin(y))
sum from n=0 to infinity of ((x^n))/n	\sum\:_{n=0}^{\infty\:}\frac{(x^{n})}{n}
(dy)/(dt)=-\sqrt[3]{y},y(0)=27	\frac{dy}{dt}=-\sqrt[3]{y},y(0)=27
(dy)/(yln(k/y))=cdx	\frac{dy}{y\ln(\frac{k}{y})}=cdx
derivative of (2x+1)^{10}	derivative\:(2x+1)^{10}
integral from 0 to infinity of e^{-2x^2}	\int\:_{0}^{\infty\:}e^{-2x^{2}}dx
integral of sec^2(4xta)n^34x	\int\:\sec^{2}(4xta)n^{3}4xdx
laplacetransform 5e^{2t}	laplacetransform\:5e^{2t}
derivative of 1/(2sqrt(1+x))	\frac{d}{dx}(\frac{1}{2\sqrt{1+x}})
(\partial)/(\partial x)(x^2-2xy+2y^2+x-2y)	\frac{\partial\:}{\partial\:x}(x^{2}-2xy+2y^{2}+x-2y)
derivative of cos(pi*x)	\frac{d}{dx}(\cos(π\cdot\:x))

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