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Popular Calculus Problems

limit as x approaches (pi/2)+of 9e^{tan(x)}	\lim\:_{x\to\:(\frac{π}{2})+}(9e^{\tan(x)})
derivative of sqrt(5x^4+x^2)	\frac{d}{dx}(\sqrt{5x^{4}+x^{2}})
integral of (y^2)/((49-y^2)^{3/2)}	\int\:\frac{y^{2}}{(49-y^{2})^{\frac{3}{2}}}dy
integral of (3x-6)e^{x^2-4x}	\int\:(3x-6)e^{x^{2}-4x}dx
derivative of cos^2(x)sin^2(x)	derivative\:\cos^{2}(x)\sin^{2}(x)
sum from n=1 to infinity of (n!)/(105^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{105^{n}}
(\partial)/(\partial x)(x^2-3xy)	\frac{\partial\:}{\partial\:x}(x^{2}-3xy)
xsqrt(1-y^2)dx=dy	x\sqrt{1-y^{2}}dx=dy
limit as x approaches 0+of ln(-x)	\lim\:_{x\to\:0+}(\ln(-x))
sum from n=0 to infinity of n/(n^2+1)x^n	\sum\:_{n=0}^{\infty\:}\frac{n}{n^{2}+1}x^{n}
integral from-2 to 3 of (23)/(x^4)	\int\:_{-2}^{3}\frac{23}{x^{4}}dx
integral of-x/(x^2+9)	\int\:-\frac{x}{x^{2}+9}dx
integral of (x^3)/(x^4+7)	\int\:\frac{x^{3}}{x^{4}+7}dx
limit as x approaches 1 of arctan^2(x)	\lim\:_{x\to\:1}(\arctan^{2}(x))
(\partial)/(\partial x)((sin^2(x))+y)	\frac{\partial\:}{\partial\:x}((\sin^{2}(x))+y)
slope of 3t-t^2	slope\:3t-t^{2}
derivative of cos(ln(sec(e^{-2x})))	\frac{d}{dx}(\cos(\ln(\sec(e^{-2x}))))
derivative of f(x)=(5x-5)(sqrt(x)+3)	derivative\:f(x)=(5x-5)(\sqrt{x}+3)
derivative of x/(1+x^3)	\frac{d}{dx}(\frac{x}{1+x^{3}})
limit as x approaches 0 of (1-4x)^{8/x}	\lim\:_{x\to\:0}((1-4x)^{\frac{8}{x}})
limit as x approaches 4 of 1/(2+sqrt(x))	\lim\:_{x\to\:4}(\frac{1}{2+\sqrt{x}})
derivative of y=sin^2(e^{sin^2(t)})	derivative\:y=\sin^{2}(e^{\sin^{2}(t)})
integral of cos(2x)e^{-x}	\int\:\cos(2x)e^{-x}dx
integral of (3x)/(sqrt(x+4))	\int\:\frac{3x}{\sqrt{x+4}}dx
integral from 0 to t of-5e^ssin(t-s)	\int\:_{0}^{t}-5e^{s}\sin(t-s)ds
integral of (x+2)(x-7)	\int\:(x+2)(x-7)dx
f(x)=e^{x^2-4}+3x+5	f(x)=e^{x^{2}-4}+3x+5
integral of (2x^2-6)/(x^3+x)	\int\:\frac{2x^{2}-6}{x^{3}+x}dx
integral of (x^2sqrt(x^3+5))	\int\:(x^{2}\sqrt{x^{3}+5})dx
slope of (3,4),(8,-3)	slope\:(3,4),(8,-3)
limit as x approaches 3 of 2x^2+x-7	\lim\:_{x\to\:3}(2x^{2}+x-7)
integral of sqrt(x^2-36)	\int\:\sqrt{x^{2}-36}dx
parity ln(sqrt((1-sin(x))/(1+sin(x))))	parity\:\ln(\sqrt{\frac{1-\sin(x)}{1+\sin(x)}})
derivative of 5^2	\frac{d}{dx}(5^{2})
(\partial)/(\partial x)(rcos(θ))	\frac{\partial\:}{\partial\:x}(r\cos(θ))
integral from 1 to 6 of (5^{ln(x)})/x	\int\:_{1}^{6}\frac{5^{\ln(x)}}{x}dx
sum from n=0 to infinity of 3(3/2)^n	\sum\:_{n=0}^{\infty\:}3(\frac{3}{2})^{n}
integral of (1/x-6/(x^2+1))	\int\:(\frac{1}{x}-\frac{6}{x^{2}+1})dx
integral from 0 to 16 of sqrt(x)-1/4 x	\int\:_{0}^{16}\sqrt{x}-\frac{1}{4}xdx
derivative of (4x+5/8)	\frac{d}{dx}(\frac{4x+5}{8})
slope of y= 3/x ,(5, 3/5)	slope\:y=\frac{3}{x},(5,\frac{3}{5})
inverse oflaplace (s-1)/(s(s+1)(s+2))	inverselaplace\:\frac{s-1}{s(s+1)(s+2)}
integral of 1/(sqrt(3-5x^2))	\int\:\frac{1}{\sqrt{3-5x^{2}}}dx
(\partial)/(\partial x)(x^3-12xy+8y^3)	\frac{\partial\:}{\partial\:x}(x^{3}-12xy+8y^{3})
derivative of (x^2-5x+1)^4	derivative\:(x^{2}-5x+1)^{4}
integral from 1 to 3 of (2x^2-12x+13)	\int\:_{1}^{3}(2x^{2}-12x+13)dx
integral of ((sqrt(ln(x)))/x)^2	\int\:(\frac{\sqrt{\ln(x)}}{x})^{2}dx
(ln(x+2))^'	(\ln(x+2))^{\prime\:}
limit as x approaches 7-of (6x)/(x-7)	\lim\:_{x\to\:7-}(\frac{6x}{x-7})
derivative of-1.2x^2+9.6x	\frac{d}{dx}(-1.2x^{2}+9.6x)
inverse oflaplace ((1-e^{-5s}))/(s^2)	inverselaplace\:\frac{(1-e^{-5s})}{s^{2}}
integral of 1/(xln(x)sqrt(ln^2(x)-4))	\int\:\frac{1}{x\ln(x)\sqrt{\ln^{2}(x)-4}}dx
integral of ((x^2)/((7+x^3)^2))	\int\:(\frac{x^{2}}{(7+x^{3})^{2}})dx
(\partial)/(\partial x)((x*y)/(x-y))	\frac{\partial\:}{\partial\:x}(\frac{x\cdot\:y}{x-y})
tangent of f(x)=-(6x)/(x^2+1),\at x=0	tangent\:f(x)=-\frac{6x}{x^{2}+1},\at\:x=0
maclaurin x*cos(x)	maclaurin\:x\cdot\:\cos(x)
(\partial)/(\partial x)(9ye^{7x})	\frac{\partial\:}{\partial\:x}(9ye^{7x})
derivative of sqrt((x+3)/(x-3))	derivative\:\sqrt{\frac{x+3}{x-3}}
(\partial)/(\partial y)(4x+y)	\frac{\partial\:}{\partial\:y}(4x+y)
laplacetransform 7t^3	laplacetransform\:7t^{3}
integral of (e^x)/((e^x-5)(e^{2x)+1)}	\int\:\frac{e^{x}}{(e^{x}-5)(e^{2x}+1)}dx
(\partial)/(\partial y)(2x^2y^3)	\frac{\partial\:}{\partial\:y}(2x^{2}y^{3})
derivative of sqrt(2x^4-2x)	\frac{d}{dx}(\sqrt{2x^{4}-2x})
integral from 0 to 6 of e^xsin(x)	\int\:_{0}^{6}e^{x}\sin(x)dx
integral of x^2*x	\int\:x^{2}\cdot\:xdx
6y^{''}+y^'-2y=0,y(0)=5,y^'(0)=-1	6y^{\prime\:\prime\:}+y^{\prime\:}-2y=0,y(0)=5,y^{\prime\:}(0)=-1
(\partial)/(\partial x)(xcos(x))	\frac{\partial\:}{\partial\:x}(x\cos(x))
integral of (2+5x)^2	\int\:(2+5x)^{2}dx
integral of (sqrt(x)+2)	\int\:(\sqrt{x}+2)dx
derivative of 3xe^{-ax}	derivative\:3xe^{-ax}
5t^2y^{''}+ty^'-12y=0	5t^{2}y^{\prime\:\prime\:}+ty^{\prime\:}-12y=0
integral of (x^2)/(sqrt(x^6-9))	\int\:\frac{x^{2}}{\sqrt{x^{6}-9}}dx
slope of (3,0),(6,2)	slope\:(3,0),(6,2)
(\partial)/(\partial z)(1/(x^2+y^2+z^2))	\frac{\partial\:}{\partial\:z}(\frac{1}{x^{2}+y^{2}+z^{2}})
taylor e^{x^2}	taylor\:e^{x^{2}}
inverse oflaplace (s-1)/(2s^2+s+3)	inverselaplace\:\frac{s-1}{2s^{2}+s+3}
derivative of 5xe^{x^2}	\frac{d}{dx}(5xe^{x^{2}})
d/(dt)(2te^{2t})	\frac{d}{dt}(2te^{2t})
integral of x^3sqrt(121-x^2)	\int\:x^{3}\sqrt{121-x^{2}}dx
taylor 6xe^x	taylor\:6xe^{x}
derivative of 10(x^3-x)^4	derivative\:10(x^{3}-x)^{4}
derivative of sin(9cos(x))	\frac{d}{dx}(\sin(9\cos(x)))
integral of 2/(1+x^2)	\int\:\frac{2}{1+x^{2}}dx
limit as x approaches-infinity of (-1)/x	\lim\:_{x\to\:-\infty\:}(\frac{-1}{x})
integral of 1/(x^2sqrt(9x^2-4))	\int\:\frac{1}{x^{2}\sqrt{9x^{2}-4}}dx
integral of x^2e^{x^3+2}	\int\:x^{2}e^{x^{3}+2}dx
derivative of-4/(1-4x)	\frac{d}{dx}(-\frac{4}{1-4x})
taylor 1/(x-1),x=7	taylor\:\frac{1}{x-1},x=7
tangent of y=x^3-2x^2+x+7	tangent\:y=x^{3}-2x^{2}+x+7
(\partial)/(\partial x)(tan(x)y)	\frac{\partial\:}{\partial\:x}(\tan(x)y)
inverse oflaplace ((s+5))/(s^2+5s+6)	inverselaplace\:\frac{(s+5)}{s^{2}+5s+6}
integral of x^6+e^{2x}	\int\:x^{6}+e^{2x}dx
integral of (10-20x^4)csc^2(2x^5-5x)	\int\:(10-20x^{4})\csc^{2}(2x^{5}-5x)dx
(\partial)/(\partial y)(ln(x-y))	\frac{\partial\:}{\partial\:y}(\ln(x-y))
derivative of x(e^x-1)	\frac{d}{dx}(x(e^{x}-1))
derivative of-ln(x^4)	\frac{d}{dx}(-\ln(x^{4}))
integral of sqrt(1+cos(piθ))	\int\:\sqrt{1+\cos(πθ)}dθ
derivative of sqrt(x/2)	derivative\:\sqrt{\frac{x}{2}}
inverse oflaplace (2s-3)/(2s^2-8s+16)	inverselaplace\:\frac{2s-3}{2s^{2}-8s+16}
f(x)=4x^3ln(x)	f(x)=4x^{3}\ln(x)

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