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Popular Calculus Problems

integral of (x^2+17)/x	\int\:\frac{x^{2}+17}{x}dx
(\partial)/(\partial x)((5x+2y)(e^y))	\frac{\partial\:}{\partial\:x}((5x+2y)(e^{y}))
tangent of 2x^2+2x	tangent\:2x^{2}+2x
integral of e^{6x}sin(3x)	\int\:e^{6x}\sin(3x)dx
(\partial)/(\partial x)(xln(x/(y^2)))	\frac{\partial\:}{\partial\:x}(x\ln(\frac{x}{y^{2}}))
limit as n approaches infinity of ln(2)	\lim\:_{n\to\:\infty\:}(\ln(2))
(dy)/(dx)+4xy=8x^3	\frac{dy}{dx}+4xy=8x^{3}
derivative of (cos(x)/5)	\frac{d}{dx}(\frac{\cos(x)}{5})
limit as x approaches infinity of (2x)/1	\lim\:_{x\to\:\infty\:}(\frac{2x}{1})
integral of (2x+3)/(x(x^2-4)^2)	\int\:\frac{2x+3}{x(x^{2}-4)^{2}}dx
(dy)/(dt)(t)+2y=3e^{-t}	\frac{dy}{dt}(t)+2y=3e^{-t}
(\partial)/(\partial x)(cos(2x+y))	\frac{\partial\:}{\partial\:x}(\cos(2x+y))
derivative of 3x^2+8x	\frac{d}{dx}(3x^{2}+8x)
limit as x approaches 1 of (x+6)/(x+1)	\lim\:_{x\to\:1}(\frac{x+6}{x+1})
limit as x approaches 1 of arctan(ln(x))	\lim\:_{x\to\:1}(\arctan(\ln(x)))
derivative of 4x^3-5x^2+ln(x)	\frac{d}{dx}(4x^{3}-5x^{2}+\ln(x))
area y^2-2x=1,x-y=1	area\:y^{2}-2x=1,x-y=1
derivative of cos(t)+t^2sin(t)	derivative\:\cos(t)+t^{2}\sin(t)
derivative of f(x)=arctan(x/a)	derivative\:f(x)=\arctan(\frac{x}{a})
derivative of cosh^3(x)	\frac{d}{dx}(\cosh^{3}(x))
integral of (10x+6)	\int\:(10x+6)dx
derivative of (x^2/5)	\frac{d}{dx}(\frac{x^{2}}{5})
integral of (5ln(x))/(x^3)	\int\:\frac{5\ln(x)}{x^{3}}dx
y^{''}-2y^'-15y=3cos(2x)+4x^2	y^{\prime\:\prime\:}-2y^{\prime\:}-15y=3\cos(2x)+4x^{2}
derivative of cot^2(cos(x))	derivative\:\cot^{2}(\cos(x))
(dy)/(dx)=sin(x+y)+cos(x+y)	\frac{dy}{dx}=\sin(x+y)+\cos(x+y)
(dx)/(dt)=20+38.0044-(1.3167)x	\frac{dx}{dt}=20+38.0044-(1.3167)x
integral of ((x^4+1)^2)/(x^3)	\int\:\frac{(x^{4}+1)^{2}}{x^{3}}dx
derivative of y= 5/(sqrt(x))	derivative\:y=\frac{5}{\sqrt{x}}
(\partial)/(\partial x)(ydx)	\frac{\partial\:}{\partial\:x}(ydx)
integral of xln((x+2)/(x+1))	\int\:x\ln(\frac{x+2}{x+1})dx
integral of (4x)/y	\int\:\frac{4x}{y}dx
derivative of sqrt(x)*e^{-x}	\frac{d}{dx}(\sqrt{x}\cdot\:e^{-x})
(dy)/(dx)=9xe^y,y(0)=0	\frac{dy}{dx}=9xe^{y},y(0)=0
tangent of f(x)=2x^2-1,\at x=-1	tangent\:f(x)=2x^{2}-1,\at\:x=-1
(dy)/(dx)=x^2y-y+x^2-1	\frac{dy}{dx}=x^{2}y-y+x^{2}-1
integral of 3x^4	\int\:3x^{4}dx
inverse oflaplace 1/(s^2(s^2+1))	inverselaplace\:\frac{1}{s^{2}(s^{2}+1)}
derivative of-(2x/((x^2+4)^2))	\frac{d}{dx}(-\frac{2x}{(x^{2}+4)^{2}})
integral of sqrt(x^5)sin(3+x^{7/2})	\int\:\sqrt{x^{5}}\sin(3+x^{\frac{7}{2}})dx
(\partial)/(\partial y)(ln((x+y)/(x-y)))	\frac{\partial\:}{\partial\:y}(\ln(\frac{x+y}{x-y}))
tangent of f(x)= 7/x ,\at x=2\lor ,x=7	tangent\:f(x)=\frac{7}{x},\at\:x=2\lor\:,x=7
integral of (2cos(x))/(sin(x))	\int\:\frac{2\cos(x)}{\sin(x)}dx
derivative of x^2+4y,3x	\frac{d}{dx}(x^{2}+4y,3x)
integral from 0 to pi/2 of cos^3(15x)	\int\:_{0}^{\frac{π}{2}}\cos^{3}(15x)dx
derivative of sqrt(11arctan(x))	\frac{d}{dx}(\sqrt{11\arctan(x)})
integral of 1/(tan(u))	\int\:\frac{1}{\tan(u)}du
limit as x approaches infinity of 1-x	\lim\:_{x\to\:\infty\:}(1-x)
laplacetransform sin(2(t-(5pi)/2))	laplacetransform\:\sin(2(t-\frac{5π}{2}))
derivative of sqrt(6-9x)	\frac{d}{dx}(\sqrt{6-9x})
derivative of f(x)=e^{4x}cos(7x)	derivative\:f(x)=e^{4x}\cos(7x)
laplacetransform sin(4t+5)	laplacetransform\:\sin(4t+5)
tangent of f(x)=-x^3,(-2,8)	tangent\:f(x)=-x^{3},(-2,8)
integral of cos(x^2)2x	\int\:\cos(x^{2})2xdx
sum from n=1 to infinity of 1/n-1/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{1}{n}-\frac{1}{n+1}
integral of (e^{5x})/(e^{5x)+6}	\int\:\frac{e^{5x}}{e^{5x}+6}dx
tangent of-2xy-4x^4=-2+y	tangent\:-2xy-4x^{4}=-2+y
(\partial)/(\partial x)(12xy-x^3-y^3-7)	\frac{\partial\:}{\partial\:x}(12xy-x^{3}-y^{3}-7)
derivative of (18x+8x^2/((9+8x)^2))	\frac{d}{dx}(\frac{18x+8x^{2}}{(9+8x)^{2}})
integral of (cot(x))/(sin(x))	\int\:\frac{\cot(x)}{\sin(x)}dx
inverse oflaplace {(2/s-1/(s^3))^2}	inverselaplace\:\left\{(\frac{2}{s}-\frac{1}{s^{3}})^{2}\right\}
derivative of 8x^2(1-3x^5)	\frac{d}{dx}(8x^{2}(1-3x)^{5})
integral of x^2sec(x^3)	\int\:x^{2}\sec(x^{3})dx
integral of (sin(2x))e^{sin^2(x)}	\int\:(\sin(2x))e^{\sin^{2}(x)}dx
(sin(3x))^'	(\sin(3x))^{\prime\:}
limit as x approaches 1 of 4x-3	\lim\:_{x\to\:1}(4x-3)
integral of sin(4xy)	\int\:\sin(4xy)dx
taylor (1-x)^2	taylor\:(1-x)^{2}
derivative of x^4(2x-5^6)	\frac{d}{dx}(x^{4}(2x-5)^{6})
f(x)=(4x^2-1)/(x^3)	f(x)=\frac{4x^{2}-1}{x^{3}}
area x=sqrt(1/(12y)),y=x,x=16y	area\:x=\sqrt{\frac{1}{12y}},y=x,x=16y
(\partial)/(\partial x)(-(x/y))	\frac{\partial\:}{\partial\:x}(-(\frac{x}{y}))
derivative of x/(4-sqrt(16-x^2))	\frac{d}{dx}(\frac{x}{4-\sqrt{16-x^{2}}})
tangent of f(x)=5-2x^2,(-5,-45)	tangent\:f(x)=5-2x^{2},(-5,-45)
integral from 0 to 2 of (1+x)^{1/3}*2	\int\:_{0}^{2}(1+x)^{\frac{1}{3}}\cdot\:2dx
xy'+(1+x*cot(x))y=0	xy\prime\:+(1+x\cdot\:\cot(x))y=0
derivative of (x-1^2(x+2))	\frac{d}{dx}((x-1)^{2}(x+2))
area y=3-x^2,y=11-6x	area\:y=3-x^{2},y=11-6x
integral from 0 to 4 of x/(sqrt(1+2x))	\int\:_{0}^{4}\frac{x}{\sqrt{1+2x}}dx
derivative of-(2x)/((x^2-1)^2)	derivative\:-\frac{2x}{(x^{2}-1)^{2}}
derivative of ln(4/x)	\frac{d}{dx}(\ln(\frac{4}{x}))
derivative of 5/(2x^3)	derivative\:\frac{5}{2x^{3}}
limit as w approaches 0 of (sec(2w)-1)/(wsec(2w))	\lim\:_{w\to\:0}(\frac{\sec(2w)-1}{w\sec(2w)})
area y=sqrt(x),y=sqrt(8-x),y=0	area\:y=\sqrt{x},y=\sqrt{8-x},y=0
derivative of 2sin(x)+2cos(x)	derivative\:2\sin(x)+2\cos(x)
y^'=y^2sin(x^2),y(-2)= 1/3	y^{\prime\:}=y^{2}\sin(x^{2}),y(-2)=\frac{1}{3}
limit as x approaches 0 of g(x)(f(x))	\lim\:_{x\to\:0}(g(x)(f(x)))
integral from 0 to 1 of (e^x)/x	\int\:_{0}^{1}\frac{e^{x}}{x}dx
derivative of (x^2+40x/5)	\frac{d}{dx}(\frac{x^{2}+40x}{5})
area f(x)=2+x-x^2,0,3	area\:f(x)=2+x-x^{2},0,3
limit as h approaches 0 of 8x+4h+9	\lim\:_{h\to\:0}(8x+4h+9)
derivative of x^3-3x-sqrt(x)	\frac{d}{dx}(x^{3}-3x-\sqrt{x})
integral of 1/(3+2cos(x)+3sin(x))	\int\:\frac{1}{3+2\cos(x)+3\sin(x)}dx
derivative of arccos(2x)	derivative\:\arccos(2x)
tangent of f(x)=sqrt(x+6),\at x=1	tangent\:f(x)=\sqrt{x+6},\at\:x=1
derivative of (x^2)/(7+6x)	derivative\:\frac{x^{2}}{7+6x}
derivative of sqrt({R)(x(x)^2-x^2})	\frac{d}{dx}(\sqrt{{R}(x)(x)^{2}-x^{2}})
integral of (sec^2(1/x))/(x^2)	\int\:\frac{\sec^{2}(\frac{1}{x})}{x^{2}}dx
integral of (cot^5(β))/(sqrt(sin(β)))	\int\:\frac{\cot^{5}(β)}{\sqrt{\sin(β)}}dβ
integral of x/((8-x^2)^2)	\int\:\frac{x}{(8-x^{2})^{2}}dx

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