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Popular Calculus Problems

derivative of sqrt(x^2+5x)	\frac{d}{dx}(\sqrt{x^{2}+5x})
integral from 0 to pi of sin(x/2)	\int\:_{0}^{π}\sin(\frac{x}{2})dx
integral of (1+sqrt(x^2+1))/((x^2+1)^{3/2)}	\int\:\frac{1+\sqrt{x^{2}+1}}{(x^{2}+1)^{\frac{3}{2}}}dx
integral of 17xe^{-x^2}	\int\:17xe^{-x^{2}}dx
(dy)/(dx)=(cos(13x))/(e^{13y)}	\frac{dy}{dx}=\frac{\cos(13x)}{e^{13y}}
integral of 7^{-2x}	\int\:7^{-2x}dx
derivative of sqrt(5x-2)	\frac{d}{dx}(\sqrt{5x-2})
limit as x approaches infinity of (2)^x	\lim\:_{x\to\:\infty\:}((2)^{x})
(dy)/(dx)-4y=2xy^2	\frac{dy}{dx}-4y=2xy^{2}
derivative of sin(x^k)	derivative\:\sin(x^{k})
integral from 0 to ln(2) of 3/(e^x+4)	\int\:_{0}^{\ln(2)}\frac{3}{e^{x}+4}dx
f(x)=x^2-4x-4	f(x)=x^{2}-4x-4
derivative of sqrt(0^4)	\frac{d}{dx}(\sqrt{0^{4}})
derivative of (5x^3-1^3ln(x^2+1))	\frac{d}{dx}((5x^{3}-1)^{3}\ln(x^{2}+1))
integral of 3xsin(x)	\int\:3x\sin(x)dx
limit as x approaches 0 of x^6cos(8/x)	\lim\:_{x\to\:0}(x^{6}\cos(\frac{8}{x}))
derivative of f(x)=(x^5)/(10)+1/(6x^3)	derivative\:f(x)=\frac{x^{5}}{10}+\frac{1}{6x^{3}}
integral from 0 to 2 of (x^2)/(x+1)	\int\:_{0}^{2}\frac{x^{2}}{x+1}dx
derivative of 4tan(x^2+x+3)	\frac{d}{dx}(4\tan(x^{2}+x+3))
derivative of y=(x^3)/6+1/(2x)	derivative\:y=\frac{x^{3}}{6}+\frac{1}{2x}
derivative of x-cos(x)	derivative\:x-\cos(x)
integral from 0 to 2 of 6t	\int\:_{0}^{2}6tdt
(\partial)/(\partial x)(1/(x-3))	\frac{\partial\:}{\partial\:x}(\frac{1}{x-3})
(\partial)/(\partial x)(sqrt((2x-3y)^3))	\frac{\partial\:}{\partial\:x}(\sqrt{(2x-3y)^{3}})
sum from n=1 to infinity}(x^{2n of)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{x^{2n}}{n!}
integral of x/(x^2-2)	\int\:\frac{x}{x^{2}-2}dx
laplacetransform 5sin(5t)sin(100t)	laplacetransform\:5\sin(5t)\sin(100t)
derivative of (6t+1)/(6t-1)	derivative\:\frac{6t+1}{6t-1}
limit as x approaches 0 of (2x^2+3x)/x	\lim\:_{x\to\:0}(\frac{2x^{2}+3x}{x})
inverse oflaplace (6s+6)/(2s^2+1)	inverselaplace\:\frac{6s+6}{2s^{2}+1}
y^'e^{9x}=0	y^{\prime\:}e^{9x}=0
y^'+2y-y^2=0	y^{\prime\:}+2y-y^{2}=0
integral of (x^2)/((x+2)^6)	\int\:\frac{x^{2}}{(x+2)^{6}}dx
integral of (x^2)/(2+x^3)	\int\:\frac{x^{2}}{2+x^{3}}dx
limit as x approaches 3 of 2x^2+3x-1	\lim\:_{x\to\:3}(2x^{2}+3x-1)
derivative of 2(e^{(sin(w))/3}+1)^{0.5}	derivative\:2(e^{\frac{\sin(w)}{3}}+1)^{0.5}
integral of (sqrt(t))/(t+1)	\int\:\frac{\sqrt{t}}{t+1}dt
derivative of 4x^{-1/2}	\frac{d}{dx}(4x^{-\frac{1}{2}})
limit as t approaches 0 of (1-cos(3t))/t	\lim\:_{t\to\:0}(\frac{1-\cos(3t)}{t})
(\partial)/(\partial x)(5(y-2)*(x-4)^3)	\frac{\partial\:}{\partial\:x}(5(y-2)\cdot\:(x-4)^{3})
derivative of 1/3 tan^3(x+tan^2(2x))	\frac{d}{dx}(\frac{1}{3}\tan^{3}(x)+\tan^{2}(2x))
integral of 1/(sqrt(u^2+1))	\int\:\frac{1}{\sqrt{u^{2}+1}}du
(\partial)/(\partial x)((-2x)/((x+y)^2))	\frac{\partial\:}{\partial\:x}(\frac{-2x}{(x+y)^{2}})
integral of 1/((sqrt(x^2+y^2))^3)	\int\:\frac{1}{(\sqrt{x^{2}+y^{2}})^{3}}dy
integral of cos(t^3)	\int\:\cos(t^{3})dt
limit as x approaches infinity of \sqrt[x]{2}-1	\lim\:_{x\to\:\infty\:}(\sqrt[x]{2}-1)
derivative of ln(9x^6)	\frac{d}{dx}(\ln(9)x^{6})
integral of (-3v+4)	\int\:(-3v+4)dv
integral of e^{2x}(2x+1)	\int\:e^{2x}(2x+1)dx
tangent of y=(-2x)/(x^2+1)	tangent\:y=\frac{-2x}{x^{2}+1}
(dy)/(dx)+6x^5y=x^5	\frac{dy}{dx}+6x^{5}y=x^{5}
(\partial)/(\partial z)(10e^xsin(y)z^3)	\frac{\partial\:}{\partial\:z}(10e^{x}\sin(y)z^{3})
derivative of (Ax^2+Bx+C(e^{4x}))	\frac{d}{dx}((Ax^{2}+Bx+C)(e^{4x}))
y^'=(2y^4-2)/(4xy^3)	y^{\prime\:}=\frac{2y^{4}-2}{4xy^{3}}
sum from n=3 to infinity of 1+1/(n^2)	\sum\:_{n=3}^{\infty\:}1+\frac{1}{n^{2}}
taylor x*e^x	taylor\:x\cdot\:e^{x}
derivative of x^2+1/x	\frac{d}{dx}(x^{2}+\frac{1}{x})
(\|x\|)^'	(\left\|x\right\|)^{\prime\:}
(\partial)/(\partial x)(cos(y)cos(x))	\frac{\partial\:}{\partial\:x}(\cos(y)\cos(x))
integral of arctan(4x)	\int\:\arctan(4x)dx
derivative of f(x)=(1-x)/(2+x)	derivative\:f(x)=\frac{1-x}{2+x}
limit as x approaches 2 of ln(x-1)	\lim\:_{x\to\:2}(\ln(x-1))
integral of cos^7(θ)sin(θ)	\int\:\cos^{7}(θ)\sin(θ)dθ
maclaurin 1/((1+x)^3)	maclaurin\:\frac{1}{(1+x)^{3}}
derivative of ln((4x+3)/(3x-5))	derivative\:\ln(\frac{4x+3}{3x-5})
integral from 0 to 3 of \|2x-1\|	\int\:_{0}^{3}\left\|2x-1\right\|dx
(x^2+1)(dy)/(dx)=xy	(x^{2}+1)\frac{dy}{dx}=xy
integral of (x^2)/(1+2x^2)	\int\:\frac{x^{2}}{1+2x^{2}}dx
integral from 2 to infinity of-5x^{-2}	\int\:_{2}^{\infty\:}-5x^{-2}dx
derivative of 5xe^{4x}	\frac{d}{dx}(5xe^{4x})
(\partial)/(\partial x)((63)/((9+x^2+y^2)))	\frac{\partial\:}{\partial\:x}(\frac{63}{(9+x^{2}+y^{2})})
(\partial)/(\partial z)(1/(x^2yz))	\frac{\partial\:}{\partial\:z}(\frac{1}{x^{2}yz})
integral of sqrt(9+4x^2)	\int\:\sqrt{9+4x^{2}}dx
inverse oflaplace ((s+2))/(s^2+s+1)-1/s	inverselaplace\:\frac{(s+2)}{s^{2}+s+1}-\frac{1}{s}
derivative of 5.2x+2.3	derivative\:5.2x+2.3
integral of ()/y	\int\:\frac{dy}{y}dx
(e^{cos(x)})^'	(e^{\cos(x)})^{\prime\:}
derivative of y=3tan^2(7x)	derivative\:y=3\tan^{2}(7x)
derivative of ln\|4+t-t^3\|	derivative\:\ln\left\|4+t-t^{3}\right\|
(\partial)/(\partial x)(x^3-3x+y^3-3y)	\frac{\partial\:}{\partial\:x}(x^{3}-3x+y^{3}-3y)
integral of (3x+7)/(x^2+5x+6)	\int\:\frac{3x+7}{x^{2}+5x+6}dx
integral of (3x-8)^{21}	\int\:(3x-8)^{21}dx
sum from n=4 to infinity of (3^n)/(10^n)	\sum\:_{n=4}^{\infty\:}\frac{3^{n}}{10^{n}}
integral of \sqrt[5]{x^2}	\int\:\sqrt[5]{x^{2}}dx
integral of sqrt(4-t^2)	\int\:\sqrt{4-t^{2}}dt
d/(dy)(sqrt(4y-1))	\frac{d}{dy}(\sqrt{4y-1})
limit as x approaches 3-of x^2-5x+6	\lim\:_{x\to\:3-}(x^{2}-5x+6)
tangent of f(x)=x^4-20x^2+64	tangent\:f(x)=x^{4}-20x^{2}+64
d/(dy)(sin(xy))	\frac{d}{dy}(\sin(xy))
integral of (6x+5)/((6x^2+10x)^5)	\int\:\frac{6x+5}{(6x^{2}+10x)^{5}}dx
derivative of (x+1(2x+1)(3x+1))	\frac{d}{dx}((x+1)(2x+1)(3x+1))
limit as x approaches 0 of-3	\lim\:_{x\to\:0}(-3)
d/(dt)(e^{t/7}sin(t/7))	\frac{d}{dt}(e^{\frac{t}{7}}\sin(\frac{t}{7}))
(\partial)/(\partial x)(y+2/(x^2))	\frac{\partial\:}{\partial\:x}(y+\frac{2}{x^{2}})
tangent of 7x^2+xy+7y^2=15,(1,1)	tangent\:7x^{2}+xy+7y^{2}=15,(1,1)
limit as x approaches 0+of (e^x+x)^{1/x}	\lim\:_{x\to\:0+}((e^{x}+x)^{\frac{1}{x}})
limit as x approaches 3 of (x^2-3)/(x-3)	\lim\:_{x\to\:3}(\frac{x^{2}-3}{x-3})
integral of (20x)/(sqrt(1-x^4))	\int\:\frac{20x}{\sqrt{1-x^{4}}}dx
integral of 1/(4+2x)	\int\:\frac{1}{4+2x}dx
tangent of y=x^3+7x-5,(1,3)	tangent\:y=x^{3}+7x-5,(1,3)

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