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Popular Calculus Problems

derivative of (3x^2+9/(6x))	\frac{d}{dx}(\frac{3x^{2}+9}{6x})
f(x)=(sqrt(x)+1)/(x^2+1)	f(x)=\frac{\sqrt{x}+1}{x^{2}+1}
derivative of e^{5x}	derivative\:e^{5x}
integral from 0 to 1 of 1/(x^2)	\int\:_{0}^{1}\frac{1}{x^{2}}dx
integral of (tan^2(x))/(sec^2(x))	\int\:\frac{\tan^{2}(x)}{\sec^{2}(x)}dx
integral of (2x+1)/(sqrt(x-2))	\int\:\frac{2x+1}{\sqrt{x-2}}dx
y^'=y(y^3-1)	y^{\prime\:}=y(y^{3}-1)
integral of (e^{-x}-e^5)*(e^x+e^{-2})	\int\:(e^{-x}-e^{5})\cdot\:(e^{x}+e^{-2})dx
y^'-y=10te^{2t},y(0)=1	y^{\prime\:}-y=10te^{2t},y(0)=1
derivative of f(x)=(-25x^2+36)^2	derivative\:f(x)=(-25x^{2}+36)^{2}
integral from 0 to 2pi of sin^2(13x)	\int\:_{0}^{2π}\sin^{2}(13x)dx
integral of xcos^2(3x)	\int\:x\cos^{2}(3x)dx
integral of (1-t)^2	\int\:(1-t)^{2}dt
derivative of (x^3-x(2x-x^2))	\frac{d}{dx}((x^{3}-x)(2x-x^{2}))
2y+(dy)/(dx)=y^2+1	2y+\frac{dy}{dx}=y^{2}+1
h(x)= 3/(x^2)+10x^3-2sin(3x)	h(x)=\frac{3}{x^{2}}+10x^{3}-2\sin(3x)
integral of sqrt((2+3x)/(x-3))	\int\:\sqrt{\frac{2+3x}{x-3}}dx
taylor ln(1-7x),0	taylor\:\ln(1-7x),0
integral of (2x)/3+3	\int\:\frac{2x}{3}+3dx
taylor 1/(1-x),14	taylor\:\frac{1}{1-x},14
(\partial)/(\partial y)(x^4y^4)	\frac{\partial\:}{\partial\:y}(x^{4}y^{4})
integral of 3χ^5sqrt(χ^3+1)	\int\:3χ^{5}\sqrt{χ^{3}+1}dχ
sum from n=3 to infinity of 1/(nln(n))	\sum\:_{n=3}^{\infty\:}\frac{1}{n\ln(n)}
integral of e^{2x}(1-6e^{2x})^2	\int\:e^{2x}(1-6e^{2x})^{2}dx
integral of 1/(y^2+4)	\int\:\frac{1}{y^{2}+4}dy
derivative of sqrt(z)	derivative\:\sqrt{z}
derivative of x(x^2+6)(x+9)	derivative\:x(x^{2}+6)(x+9)
tangent of f(x)=e^{4x}cos(pix),\at x=0	tangent\:f(x)=e^{4x}\cos(πx),\at\:x=0
taylor cos(3x)	taylor\:\cos(3x)
integral of x^9+8	\int\:x^{9}+8dx
xy^'=7	xy^{\prime\:}=7
(\partial)/(\partial y)(3x^2e^{x^2y})	\frac{\partial\:}{\partial\:y}(3x^{2}e^{x^{2}y})
area f(x)=cos(x),0, pi/2	area\:f(x)=\cos(x),0,\frac{π}{2}
limit as x approaches infinity of-3x^2+5	\lim\:_{x\to\:\infty\:}(-3x^{2}+5)
integral of xe^{x^{-2}}	\int\:xe^{x^{-2}}dx
derivative of 3/(x^2+1)	\frac{d}{dx}(\frac{3}{x^{2}+1})
derivative of 1/(x^6+1/(x^7))	\frac{d}{dx}(\frac{1}{x^{6}}+\frac{1}{x^{7}})
derivative of (x^2+8)(5-x)	derivative\:(x^{2}+8)(5-x)
tangent of f(x)=(-8x)/(x^2+1),(-1,4)	tangent\:f(x)=\frac{-8x}{x^{2}+1},(-1,4)
integral of (tan(x))/(csc(x)+cot(x))	\int\:\frac{\tan(x)}{\csc(x)+\cot(x)}dx
derivative of 4x^5+2x^3+6x^2+3x	\frac{d}{dx}(4x^{5}+2x^{3}+6x^{2}+3x)
integral of 8e^{2θ}sin(2θ)	\int\:8e^{2θ}\sin(2θ)dθ
y^'+y=x*e^{-x}+1	y^{\prime\:}+y=x\cdot\:e^{-x}+1
tangent of 2x^3+36x^2+210x+11	tangent\:2x^{3}+36x^{2}+210x+11
integral of ax^3	\int\:ax^{3}dx
integral of (6x^2+4x-30)/(x^3+5x^2+6x)	\int\:\frac{6x^{2}+4x-30}{x^{3}+5x^{2}+6x}dx
integral from 3 to 4 of 1/(x^2-4)	\int\:_{3}^{4}\frac{1}{x^{2}-4}dx
derivative of f(x)=5x^2-3x+7	derivative\:f(x)=5x^{2}-3x+7
integral of 1/(4+2sin(x))	\int\:\frac{1}{4+2\sin(x)}dx
derivative of e^{-5x^2}	derivative\:e^{-5x^{2}}
limit as x approaches-4 of 15	\lim\:_{x\to\:-4}(15)
sum from n=1 to infinity of (1/2)^2	\sum\:_{n=1}^{\infty\:}(\frac{1}{2})^{2}
x^{''}-2x^'+x=24t^2e^t	x^{\prime\:\prime\:}-2x^{\prime\:}+x=24t^{2}e^{t}
f(x)=x^{8x}	f(x)=x^{8x}
integral of (sec^2(8x))/(tan(8x)-6)	\int\:\frac{\sec^{2}(8x)}{\tan(8x)-6}dx
(dy)/(dx)=xe^{x^2-4}	\frac{dy}{dx}=xe^{x^{2}-4}
sum from n=1 to infinity of (-8)^{-n}	\sum\:_{n=1}^{\infty\:}(-8)^{-n}
(\partial)/(\partial z)(e^{xy}sin(z))	\frac{\partial\:}{\partial\:z}(e^{xy}\sin(z))
integral of (x^2+3x)^4(2x+3)	\int\:(x^{2}+3x)^{4}(2x+3)dx
laplacetransform 4-2e^{-4t}	laplacetransform\:4-2e^{-4t}
((ln(x))/x)^'	(\frac{\ln(x)}{x})^{\prime\:}
limit as x approaches+4 of sqrt(x)-2	\lim\:_{x\to\:+4}(\sqrt{x}-2)
integral from 0 to pi of (xcos(2x))	\int\:_{0}^{π}(x\cos(2x))dx
(dy)/(dt)-0.1y=-t	\frac{dy}{dt}-0.1y=-t
derivative of (9-x^2/((9+x^2)^2))	\frac{d}{dx}(\frac{9-x^{2}}{(9+x^{2})^{2}})
derivative of 1/(sin^2(x))	derivative\:\frac{1}{\sin^{2}(x)}
integral of x^2sqrt(9+x)	\int\:x^{2}\sqrt{9+x}dx
slope of x/(x^2+1)	slope\:\frac{x}{x^{2}+1}
(x^2+1)(dy)/(dx)+6x(y-1)=0,y(0)=8	(x^{2}+1)\frac{dy}{dx}+6x(y-1)=0,y(0)=8
integral of (x+6)^4	\int\:(x+6)^{4}dx
area y=x,y=sqrt(x),x=0,x=2	area\:y=x,y=\sqrt{x},x=0,x=2
derivative of f(x)=xsqrt(x^2+1)	derivative\:f(x)=x\sqrt{x^{2}+1}
laplacetransform (t^2-1)^2	laplacetransform\:(t^{2}-1)^{2}
derivative of x^{e^{x^2}}	\frac{d}{dx}(x^{e^{x^{2}}})
limit as x approaches-19+of sqrt(x+19)	\lim\:_{x\to\:-19+}(\sqrt{x+19})
derivative of y=arccos(2x)	derivative\:y=\arccos(2x)
integral of e^{inx}	\int\:e^{inx}dx
integral of-ye^{-y}	\int\:-ye^{-y}dy
integral of 5/(1+x^2)	\int\:\frac{5}{1+x^{2}}dx
derivative of (sqrt(x)/(8+x))	\frac{d}{dx}(\frac{\sqrt{x}}{8+x})
sum from n=0 to infinity of 10(x/3)^n	\sum\:_{n=0}^{\infty\:}10(\frac{x}{3})^{n}
limit as x approaches+2 of (2-x)/(x^2-4)	\lim\:_{x\to\:+2}(\frac{2-x}{x^{2}-4})
integral of ((5x+4))/(sqrt(5x-1))	\int\:\frac{(5x+4)}{\sqrt{5x-1}}dx
derivative of 5/((x^2-3x^2))	\frac{d}{dx}(\frac{5}{(x^{2}-3x)^{2}})
derivative of 16t^2	derivative\:16t^{2}
area ((3sqrt(x)))/2 ,3,2-(1/2 x)	area\:\frac{(3\sqrt{x})}{2},3,2-(\frac{1}{2}x)
derivative of (1-3x/(5+x))	\frac{d}{dx}(\frac{1-3x}{5+x})
integral of t^6(3+t^7)^6	\int\:t^{6}(3+t^{7})^{6}dt
(\partial)/(\partial x)(-e^{cos(x)}sin(x))	\frac{\partial\:}{\partial\:x}(-e^{\cos(x)}\sin(x))
derivative of 100x^{0.25}y^{0.75}	\frac{d}{dx}(100x^{0.25}y^{0.75})
integral from-1 to 1 of (e^x-(x^2-2))	\int\:_{-1}^{1}(e^{x}-(x^{2}-2))dx
(dy)/(dx)= 1/(xln(2))	\frac{dy}{dx}=\frac{1}{x\ln(2)}
derivative of 3e^{2x^2}	derivative\:3e^{2x^{2}}
integral of (9000-3000x)/((x^2-6x+10)^2)	\int\:\frac{9000-3000x}{(x^{2}-6x+10)^{2}}dx
derivative of (2x+3^3)	\frac{d}{dx}((2x+3)^{3})
tangent of f(x)= x/(x+3),\at x=-5	tangent\:f(x)=\frac{x}{x+3},\at\:x=-5
derivative of 9x^2cos(x)cot(x)	derivative\:9x^{2}\cdot\:\cos(x)\cdot\:\cot(x)
(\partial)/(\partial x)(r(θ,x)sin(θ))	\frac{\partial\:}{\partial\:x}(r(θ,x)\sin(θ))
area x=5,y=sqrt(5x)	area\:x=5,y=\sqrt{5x}
derivative of (sin(5x))/(3x)	derivative\:\frac{\sin(5x)}{3x}

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