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Popular Calculus Problems

sum from n=1 to infinity of (n!)/(2n-1)	\sum\:_{n=1}^{\infty\:}\frac{n!}{2n-1}
y^'= 5/(y+2)	y^{\prime\:}=\frac{5}{y+2}
derivative of (5x^6+8x^3^4)	\frac{d}{dx}((5x^{6}+8x^{3})^{4})
integral of csc(3x)cot(3x)	\int\:\csc(3x)\cot(3x)dx
integral of (3y^2)	\int\:(3y^{2})dy
tangent of y=x+sqrt(x),(49,56)	tangent\:y=x+\sqrt{x},(49,56)
integral from 1 to 25 of 2/x	\int\:_{1}^{25}\frac{2}{x}dx
limit as x approaches+0 of (x^2)/(1-cos(x))	\lim\:_{x\to\:+0}(\frac{x^{2}}{1-\cos(x)})
(dy)/(dx)=(5x)/(7y)	\frac{dy}{dx}=\frac{5x}{7y}
integral of 1/2 xcos(4x^2)	\int\:\frac{1}{2}x\cos(4x^{2})dx
integral of-2x+6x^2-4x^3+C	\int\:-2x+6x^{2}-4x^{3}+Cdx
(\partial)/(\partial y)(ln(1+xy))	\frac{\partial\:}{\partial\:y}(\ln(1+xy))
sum from n=1 to infinity of 1/n-1/(2n+1)	\sum\:_{n=1}^{\infty\:}\frac{1}{n}-\frac{1}{2n+1}
taylor sqrt(1-x^2),0	taylor\:\sqrt{1-x^{2}},0
derivative of sqrt(2-3x^2)	\frac{d}{dx}(\sqrt{2-3x^{2}})
derivative of f(x)=(x^2)/(1+4x)	derivative\:f(x)=\frac{x^{2}}{1+4x}
integral of 1/((arcsin(x))^3sqrt(1-x^2))	\int\:\frac{1}{(\arcsin(x))^{3}\sqrt{1-x^{2}}}dx
laplacetransform e^{4(t-3)}	laplacetransform\:e^{4(t-3)}
limit as x approaches 1-of (-1)/(x^2-1)	\lim\:_{x\to\:1-}(\frac{-1}{x^{2}-1})
integral of 1/(1-5x)	\int\:\frac{1}{1-5x}dx
(dr)/(dθ)r=(7+sec(θ))sin(θ)	\frac{dr}{dθ}r=(7+\sec(θ))\sin(θ)
derivative of x^2sqrt(3x+5)	derivative\:x^{2}\sqrt{3x+5}
integral of x/((x^2+7)^2)	\int\:\frac{x}{(x^{2}+7)^{2}}dx
derivative of f(x)=(-3x^3+3x^2)^3	derivative\:f(x)=(-3x^{3}+3x^{2})^{3}
limit as x approaches-1 of arccos(x)	\lim\:_{x\to\:-1}(\arccos(x))
integral from 0 to pi of 3sin^2(xco)s^4x	\int\:_{0}^{π}3\sin^{2}(xco)s^{4}xdx
limit as x approaches 7 of ((1/x-1/7))/(x-7)	\lim\:_{x\to\:7}(\frac{(\frac{1}{x}-\frac{1}{7})}{x-7})
integral of (x^3)/(x^8+16)	\int\:\frac{x^{3}}{x^{8}+16}dx
derivative of x^2(1-x^2)	\frac{d}{dx}(x^{2}(1-x)^{2})
derivative of 4sin(θ)-θ	derivative\:4\sin(θ)-θ
integral from-1 to 2 of xe^{6x}	\int\:_{-1}^{2}xe^{6x}dx
derivative of 3x^{5/2}+8x^2	derivative\:3x^{\frac{5}{2}}+8x^{2}
integral of 1/(sqrt(2pi))e^{(x^2)/2}	\int\:\frac{1}{\sqrt{2π}}e^{\frac{x^{2}}{2}}dx
limit as x approaches 3-of ln(x^2-9)	\lim\:_{x\to\:3-}(\ln(x^{2}-9))
derivative of sin(x+x*cos(x))	\frac{d}{dx}(\sin(x)+x\cdot\:\cos(x))
derivative of x^2y-x	\frac{d}{dx}(x^{2}y-x)
integral of (cos(5x)cos(3x))	\int\:(\cos(5x)\cos(3x))dx
integral from 0 to 1 of x-x^3	\int\:_{0}^{1}x-x^{3}dx
(\partial)/(\partial x)(e^{-x^3-y^3})	\frac{\partial\:}{\partial\:x}(e^{-x^{3}-y^{3}})
derivative of 5^t	derivative\:5^{t}
f(x)=sin(x^5)	f(x)=\sin(x^{5})
derivative of (-5/(x^2))	\frac{d}{dx}(\frac{-5}{x^{2}})
integral of (2x-4)/((x^2-4x+20)^2)	\int\:\frac{2x-4}{(x^{2}-4x+20)^{2}}dx
integral of x^2sqrt(ax^3-b)	\int\:x^{2}\sqrt{ax^{3}-b}dx
laplacetransform sin(5pit)	laplacetransform\:\sin(5πt)
integral of (7x^2+9x+7)/((x^2+1)^2)	\int\:\frac{7x^{2}+9x+7}{(x^{2}+1)^{2}}dx
integral from 4 to 5 of x/(x^2+4x+20)	\int\:_{4}^{5}\frac{x}{x^{2}+4x+20}dx
integral of (-5csc^2(x))	\int\:(-5\csc^{2}(x))dx
taylor xcos(2x),1	taylor\:x\cos(2x),1
limit as x approaches+1 of e^{4x^3-4x}	\lim\:_{x\to\:+1}(e^{4x^{3}-4x})
derivative of (3x^4-x/x)	\frac{d}{dx}(\frac{3x^{4}-x}{x})
integral of 30sin^3(x)cos^2(x)	\int\:30\sin^{3}(x)\cos^{2}(x)dx
integral of 5x*e^{10x}	\int\:5x\cdot\:e^{10x}dx
integral from 2 to 3 of (x-4)sqrt(5-x)	\int\:_{2}^{3}(x-4)\sqrt{5-x}dx
derivative of (x^2-49)/(x+7)	derivative\:\frac{x^{2}-49}{x+7}
integral of (3x)/(sqrt(9-25x^4))	\int\:\frac{3x}{\sqrt{9-25x^{4}}}dx
derivative of f(x)=(x^2+3)^3(x^3+3)^2	derivative\:f(x)=(x^{2}+3)^{3}(x^{3}+3)^{2}
derivative of 5x^2cos(7x)	\frac{d}{dx}(5x^{2}\cos(7x))
f^{''}(x)=x^3-4x+1,f^'(0)=2,f(1)=-2	f^{\prime\:\prime\:}(x)=x^{3}-4x+1,f^{\prime\:}(0)=2,f(1)=-2
limit as x approaches 2 of x^2-5x+6x^2-4	\lim\:_{x\to\:2}(x^{2}-5x+6x^{2}-4)
limit as x approaches 7 of (x+7)/(x-7)	\lim\:_{x\to\:7}(\frac{x+7}{x-7})
integral of cos(8x)cos(3x)	\int\:\cos(8x)\cos(3x)dx
integral of 3/(sqrt(t))	\int\:\frac{3}{\sqrt{t}}dt
derivative of ln(3x+x^2)	\frac{d}{dx}(\ln(3x+x^{2}))
derivative of-(4x/y)	\frac{d}{dx}(-\frac{4x}{y})
(\partial)/(\partial z)(xsin(yz))	\frac{\partial\:}{\partial\:z}(x\sin(yz))
integral of xarcsin(6x)	\int\:x\arcsin(6x)dx
derivative of e^{(3x/2})	\frac{d}{dx}(e^{\frac{3x}{2}})
limit as x approaches pi of ln(sin(x))	\lim\:_{x\to\:π}(\ln(\sin(x)))
integral of (sec(z)tan(z))/(sqrt(sec(z)))	\int\:\frac{\sec(z)\tan(z)}{\sqrt{\sec(z)}}dz
derivative of (1-25x^2)^2arcsin(5x)	derivative\:(1-25x^{2})^{2}\arcsin(5x)
tangent of (64)/(x^2+16),\at x=3	tangent\:\frac{64}{x^{2}+16},\at\:x=3
integral from 2 to 3 of (x^2-4)	\int\:_{2}^{3}(x^{2}-4)dx
tangent of f(x)=(6x)/(2+x^2),(2,2)	tangent\:f(x)=\frac{6x}{2+x^{2}},(2,2)
integral of (sqrt(3x+2))	\int\:(\sqrt{3x+2})dx
derivative of y=19cos(x/b-2.5)+19	derivative\:y=19\cos(\frac{x}{b}-2.5)+19
(\partial)/(\partial x)(sin^2(2x+3y))	\frac{\partial\:}{\partial\:x}(\sin^{2}(2x+3y))
integral from 0 to 1 of x^2(x^3-2)^3	\int\:_{0}^{1}x^{2}(x^{3}-2)^{3}dx
(\partial)/(\partial x)(t/x)	\frac{\partial\:}{\partial\:x}(\frac{t}{x})
(dy)/(dx)+(3/x)y=-4x-10	\frac{dy}{dx}+(\frac{3}{x})y=-4x-10
integral of 1/(sqrt(x^2-4))	\int\:\frac{1}{\sqrt{x^{2}-4}}dx
(dy)/(dx)= 2/x	\frac{dy}{dx}=\frac{2}{x}
derivative of a/(1+\frac{b{x+c}})	\frac{d}{dx}(\frac{a}{1+\frac{b}{x+c}})
integral of 6x^2	\int\:6x^{2}dx
limit as x approaches 0 of x-1/(ln\|x\|)	\lim\:_{x\to\:0}(x-\frac{1}{\ln\left\|x\right\|})
x^2y^'+2xy=ln(x),y(1)=6	x^{2}y^{\prime\:}+2xy=\ln(x),y(1)=6
limit as x approaches-2-of x/(x^2-4)	\lim\:_{x\to\:-2-}(\frac{x}{x^{2}-4})
derivative of sqrt(y/2)	derivative\:\sqrt{\frac{y}{2}}
derivative of-(48x/((x^2+12)^2))	\frac{d}{dx}(-\frac{48x}{(x^{2}+12)^{2}})
integral of e^{ix}	\int\:e^{ix}dx
derivative of 1/(sin(x))	derivative\:\frac{1}{\sin(x)}
integral of sin(2θ)sin(6θ)	\int\:\sin(2θ)\sin(6θ)dθ
laplacetransform 2sin(3t)cos(3t)	laplacetransform\:2\sin(3t)\cos(3t)
integral of (z+3)^4	\int\:(z+3)^{4}dz
derivative of (3x-2)^3(8x^2+7)^3	derivative\:(3x-2)^{3}(8x^{2}+7)^{3}
area-1/2 x^3+2x^2+15/2 x-9,[1,6]	area\:-\frac{1}{2}x^{3}+2x^{2}+\frac{15}{2}x-9,[1,6]
integral from-1 to 1 of 4-4x^2	\int\:_{-1}^{1}4-4x^{2}dx
derivative of (4-2x-x^2/(x^2-6))	\frac{d}{dx}(\frac{4-2x-x^{2}}{x^{2}-6})
xv'+v=((1+2v))/(1-v)	xv\prime\:+v=\frac{(1+2v)}{1-v}
derivative of x^4ln(x)	derivative\:x^{4}\ln(x)

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