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Popular Calculus Problems

integral of 3^{-x}sin(x)	\int\:3^{-x}\sin(x)dx
y^3*(dy)/(dx)+x^3=0	y^{3}\cdot\:\frac{dy}{dx}+x^{3}=0
derivative of ((x^2+6)/(x^2-6))^4	derivative\:(\frac{x^{2}+6}{x^{2}-6})^{4}
slope of (-2,5),(3,-5)	slope\:(-2,5),(3,-5)
derivative of 7arctanh(cos(x))	\frac{d}{dx}(7\arctanh(\cos(x)))
limit as x approaches 2 of (x^4-16)/(x^3-8)	\lim\:_{x\to\:2}(\frac{x^{4}-16}{x^{3}-8})
integral of e^{2x}-1	\int\:e^{2x}-1dx
integral of (5x^2)/((121+x^2)^2)	\int\:\frac{5x^{2}}{(121+x^{2})^{2}}dx
limit as x approaches 1 of 1/(ln(x))	\lim\:_{x\to\:1}(\frac{1}{\ln(x)})
integral of 7e^x-3	\int\:7e^{x}-3dx
integral of-6t	\int\:-6tdt
limit as x approaches-2-of 3x+2	\lim\:_{x\to\:-2-}(3x+2)
integral from 1 to 5 of ln(x)	\int\:_{1}^{5}\ln(x)dx
y^{''}-5y^'+6y=2e^{-2s},y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=2e^{-2s},y(0)=0,y^{\prime\:}(0)=0
derivative of (3x^2-10)^{-14}	derivative\:(3x^{2}-10)^{-14}
derivative of x/(x^{-1+2})	\frac{d}{dx}(\frac{x}{x^{-1}+2})
integral of ((1))/((sin(x)-2csc(x)))	\int\:\frac{(1)}{(\sin(x)-2\csc(x))}dx
integral of-4e^{5x}	\int\:-4e^{5x}dx
integral of sin(2x)sin(8x)	\int\:\sin(2x)\sin(8x)dx
y^{''}+5y=0,y^'(1)=3	y^{\prime\:\prime\:}+5y=0,y^{\prime\:}(1)=3
limit as x approaches 0+of tan(x)	\lim\:_{x\to\:0+}(\tan(x))
integral of 1/(cos(2y)-cos^2(y))	\int\:\frac{1}{\cos(2y)-\cos^{2}(y)}dy
tangent of f(x)=(x-2)(x^2+4),(1,-5)	tangent\:f(x)=(x-2)(x^{2}+4),(1,-5)
area sin(x),0,pi	area\:\sin(x),0,π
derivative of 3e^{3x}	derivative\:3e^{3x}
4y^{'''}+12y^{''}-16y^'-48y=0	4y^{\prime\:\prime\:\prime\:}+12y^{\prime\:\prime\:}-16y^{\prime\:}-48y=0
tangent of f(x)=8x^3-24x^2-193x+48	tangent\:f(x)=8x^{3}-24x^{2}-193x+48
derivative of sin(x(x^2-27x+6))	\frac{d}{dx}(\sin(x)(x^{2}-27x+6))
derivative of ln(1+sqrt(x))	\frac{d}{dx}(\ln(1+\sqrt{x}))
sum from n=1 to infinity of (sin(9))^n	\sum\:_{n=1}^{\infty\:}(\sin(9))^{n}
49y^{''}+14y^'+y=0	49y^{\prime\:\prime\:}+14y^{\prime\:}+y=0
derivative of (2x^2+1^{3/2})	\frac{d}{dx}((2x^{2}+1)^{\frac{3}{2}})
integral from-2 to 1 of (8x^3-3x^2)	\int\:_{-2}^{1}(8x^{3}-3x^{2})dx
(dy)/(dx)=3xe^y	\frac{dy}{dx}=3xe^{y}
derivative of-1/2 cos(x)	\frac{d}{dx}(-\frac{1}{2}\cos(x))
tangent of (7-6x)^{1/2},\at x=-1	tangent\:(7-6x)^{\frac{1}{2}},\at\:x=-1
integral from 1 to 2 of 1/(x^3)	\int\:_{1}^{2}\frac{1}{x^{3}}dx
tangent of f(x)=x^2+x,(2,6)	tangent\:f(x)=x^{2}+x,(2,6)
derivative of cos^3(x+sin^3(x))	\frac{d}{dx}(\cos^{3}(x)+\sin^{3}(x))
limit as x approaches infinity of 3/2	\lim\:_{x\to\:\infty\:}(\frac{3}{2})
integral from 0 to pi of 2pix(sin(x))	\int\:_{0}^{π}2πx(\sin(x))dx
integral of cos(2+t)	\int\:\cos(2+t)dt
(x^2+1)y^'+3x(y-1)=0,y(0)=5	(x^{2}+1)y^{\prime\:}+3x(y-1)=0,y(0)=5
integral from 0 to infinity of e^{-x^2}	\int\:_{0}^{\infty\:}e^{-x^{2}}dx
integral of (-5)/((x^2+5)^{3/2)}	\int\:\frac{-5}{(x^{2}+5)^{\frac{3}{2}}}dx
d/(dt)(sqrt(6/5-t^2))	\frac{d}{dt}(\sqrt{\frac{6}{5}-t^{2}})
area (x^2)/8 ,2x^2,2,0	area\:\frac{x^{2}}{8},2x^{2},2,0
sum from n=1 to infinity of n!x^n	\sum\:_{n=1}^{\infty\:}n!x^{n}
d/(dy)(xysqrt(1-(x^2)/4-(y^2)/9))	\frac{d}{dy}(xy\sqrt{1-\frac{x^{2}}{4}-\frac{y^{2}}{9}})
integral of (5x^2+3x-1)/(x^3-2x^2+x-2)	\int\:\frac{5x^{2}+3x-1}{x^{3}-2x^{2}+x-2}dx
limit as x approaches 0 of (x^2-3x)/(2x)	\lim\:_{x\to\:0}(\frac{x^{2}-3x}{2x})
integral from-infinity to 0 of 15xe^{3x}	\int\:_{-\infty\:}^{0}15xe^{3x}dx
f(x)=sqrt(3x+4)	f(x)=\sqrt{3x+4}
derivative of (1+xf(x))/(sqrt(x))	derivative\:\frac{1+xf(x)}{\sqrt{x}}
integral of 1/(2-3u-u^2)	\int\:\frac{1}{2-3u-u^{2}}du
derivative of log_{2}(x+1)	\frac{d}{dx}(\log_{2}(x+1))
laplacetransform 7x^2	laplacetransform\:7x^{2}
(x^4)^'	(x^{4})^{\prime\:}
(\partial)/(\partial x)(1/2 yarctan(x/y))	\frac{\partial\:}{\partial\:x}(\frac{1}{2}y\arctan(\frac{x}{y}))
integral of (x^2-3x-7)/((2x+3)(x+1))	\int\:\frac{x^{2}-3x-7}{(2x+3)(x+1)}dx
integral from 1 to e^3 of 1/(x(1+ln(x)))	\int\:_{1}^{e^{3}}\frac{1}{x(1+\ln(x))}dx
y^{''}+25y=4csc^2(5t)	y^{\prime\:\prime\:}+25y=4\csc^{2}(5t)
(\partial)/(\partial x)(3xcos(y))	\frac{\partial\:}{\partial\:x}(3x\cos(y))
limit as x approaches 0 of 1/(cos(8x))	\lim\:_{x\to\:0}(\frac{1}{\cos(8x)})
derivative of-11(4x^3-11^{13})	\frac{d}{dx}(-11(4x^{3}-11)^{13})
tangent of (6x)/(x+3)	tangent\:\frac{6x}{x+3}
(\partial)/(\partial x)(uv^2)	\frac{\partial\:}{\partial\:x}(uv^{2})
derivative of 4x-1/(x^2)	\frac{d}{dx}(4x-\frac{1}{x^{2}})
integral of (sinh(sqrt(x)))/(sqrt(x))	\int\:\frac{\sinh(\sqrt{x})}{\sqrt{x}}dx
y^'=(1+y)^4	y^{\prime\:}=(1+y)^{4}
(dy)/(dx)=x^{5/2}y^3	\frac{dy}{dx}=x^{\frac{5}{2}}y^{3}
(\partial)/(\partial y)((2x+3y)/(y-x))	\frac{\partial\:}{\partial\:y}(\frac{2x+3y}{y-x})
integral of (e^{-bx})/(1-e^{-2bx)}	\int\:\frac{e^{-bx}}{1-e^{-2bx}}dx
integral of xln(6x)	\int\:x\ln(6x)dx
tangent of 2/(x^2)	tangent\:\frac{2}{x^{2}}
derivative of ln((x^2^2))	\frac{d}{dx}(\ln((x^{2})^{2}))
slope of (-pi,0),(-pi/2 ,4)	slope\:(-π,0),(-\frac{π}{2},4)
derivative of 2/y	derivative\:\frac{2}{y}
integral of (x^2-2)/(2x)	\int\:\frac{x^{2}-2}{2x}dx
(\partial)/(\partial x)((7x-5y)/(y^2+2x^2))	\frac{\partial\:}{\partial\:x}(\frac{7x-5y}{y^{2}+2x^{2}})
d/(dy)(3x^2y)	\frac{d}{dy}(3x^{2}y)
(dy)/(dx)+3y=0	\frac{dy}{dx}+3y=0
integral from 1 to e^4 of x^5ln(x)	\int\:_{1}^{e^{4}}x^{5}\ln(x)dx
(\partial)/(\partial y)(yarctan(x/z))	\frac{\partial\:}{\partial\:y}(y\arctan(\frac{x}{z}))
derivative of h(x)=4sqrt(x^7)	derivative\:h(x)=4\sqrt{x^{7}}
integral from 2 to 5 of (3x+3)/(x^2)	\int\:_{2}^{5}\frac{3x+3}{x^{2}}dx
limit as x approaches 1 of (7x^2-4x-3)/(3x^2-4x+1)	\lim\:_{x\to\:1}(\frac{7x^{2}-4x-3}{3x^{2}-4x+1})
derivative of 94-10cos(pi/(12(x-2)))	\frac{d}{dx}(94-10\cos(\frac{π}{12}(x-2)))
(\partial)/(\partial y)(e^{xy}cos(x+y))	\frac{\partial\:}{\partial\:y}(e^{xy}\cos(x+y))
derivative of (sin(9x)^{ln(x)})	\frac{d}{dx}((\sin(9x))^{\ln(x)})
integral of 10e^{5x}	\int\:10e^{5x}dx
derivative of tan(sqrt(cos^2(x^5)))	\frac{d}{dx}(\tan(\sqrt{\cos^{2}(x^{5})}))
limit as x approaches 0 of (7x^2-4x)/x	\lim\:_{x\to\:0}(\frac{7x^{2}-4x}{x})
d/(dt)(asin(t))	\frac{d}{dt}(a\sin(t))
laplacetransform e^2tcos(2t)	laplacetransform\:e^{2}t\cos(2t)
integral of 6/7 x^{-1/7}	\int\:\frac{6}{7}x^{-\frac{1}{7}}dx
limit as x approaches 3-of (x-3)^{-1}	\lim\:_{x\to\:3-}((x-3)^{-1})
(\partial)/(\partial y)(ln(10x^2-7y^2))	\frac{\partial\:}{\partial\:y}(\ln(10x^{2}-7y^{2}))
tangent of 2/(3\sqrt[3]{x)}	tangent\:\frac{2}{3\sqrt[3]{x}}
derivative of f(x)=(4-3x-x^2)/(x^2-1)	derivative\:f(x)=\frac{4-3x-x^{2}}{x^{2}-1}

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