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Popular Calculus Problems

f(x)=cos(cos(cos(x)))	f(x)=\cos(\cos(\cos(x)))
integral from-8 to 1 of 1/(\sqrt[3]{x)}	\int\:_{-8}^{1}\frac{1}{\sqrt[3]{x}}dx
taylor x^{-2},1	taylor\:x^{-2},1
(\partial)/(\partial y)(sqrt((x+2)/(y+1)))	\frac{\partial\:}{\partial\:y}(\sqrt{\frac{x+2}{y+1}})
integral of (x+2)(x-3)	\int\:(x+2)(x-3)dx
integral from 0 to 1 of tsqrt(4+9t^2)	\int\:_{0}^{1}t\sqrt{4+9t^{2}}dt
integral of e^-	\int\:e^{-}
derivative of 1/(sqrt(2pi)e^{(-x^2)/2})	\frac{d}{dx}(\frac{1}{\sqrt{2π}}e^{\frac{-x^{2}}{2}})
limit as x approaches 3 of (x-3)/(x+3)	\lim\:_{x\to\:3}(\frac{x-3}{x+3})
xy^'+4y=-3x	xy^{\prime\:}+4y=-3x
integral of-x/(x^2+4)	\int\:-\frac{x}{x^{2}+4}dx
integral of (-4x+10)/(x^3)	\int\:\frac{-4x+10}{x^{3}}dx
laplacetransform {0}	laplacetransform\:\left\{0\right\}
integral of (2x+5y)^6	\int\:(2x+5y)^{6}dy
integral from 0 to 1 of 2pi(x+5)x^2	\int\:_{0}^{1}2π(x+5)x^{2}dx
limit as x approaches 4 of 8-3x	\lim\:_{x\to\:4}(8-3x)
e^2x(dy)/(dx)-e^xy=e^{(-x)}y^2	e^{2}x\frac{dy}{dx}-e^{x}y=e^{(-x)}y^{2}
derivative of f(x)=2e^2	derivative\:f(x)=2e^{2}
integral of 2sin(x-1)	\int\:2\sin(x-1)dx
(dx)/(dt)=sin(pix)	\frac{dx}{dt}=\sin(πx)
derivative of ln(x^2+y^2+1)	\frac{d}{dx}(\ln(x^{2}+y^{2}+1))
limit as x approaches infinity+of ((5x^3+7x^2-8x+9))/(11x^2+7x-6)	\lim\:_{x\to\:\infty\:+}(\frac{(5x^{3}+7x^{2}-8x+9)}{11x^{2}+7x-6})
integral of sin^4(7x)	\int\:\sin^{4}(7x)dx
inverse oflaplace 1/((s-5)^2)	inverselaplace\:\frac{1}{(s-5)^{2}}
derivative of xsqrt(1+x^2)	\frac{d}{dx}(x\sqrt{1+x^{2}})
y^{''}+4y^'+13y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+13y=0
(d^2)/(dx^2)(e^{2x})	\frac{d^{2}}{dx^{2}}(e^{2x})
area f(x)=2x-4,3,6	area\:f(x)=2x-4,3,6
integral of (3x^2-7x)^4(6x-7)	\int\:(3x^{2}-7x)^{4}(6x-7)dx
derivative of 20x^{12/5}-6x^{2/13}	\frac{d}{dx}(20x^{\frac{12}{5}}-6x^{\frac{2}{13}})
inverse oflaplace (s+3)/((s+3)^2+25)	inverselaplace\:\frac{s+3}{(s+3)^{2}+25}
integral of sec^3(6x)	\int\:\sec^{3}(6x)dx
area-x,x,-2x+6	area\:-x,x,-2x+6
integral of (x-x^2)/(2\sqrt[3]{x)}	\int\:\frac{x-x^{2}}{2\sqrt[3]{x}}dx
(\partial)/(\partial x)(-5e^xln(y))	\frac{\partial\:}{\partial\:x}(-5e^{x}\ln(y))
area y=x^2,y=3x+4	area\:y=x^{2},y=3x+4
simplify-6	simplify\:-6
d/(dt)(e^t-4)	\frac{d}{dt}(e^{t}-4)
(2x-y)+(2y-x)y^'=0,y(1)=3	(2x-y)+(2y-x)y^{\prime\:}=0,y(1)=3
(\partial)/(\partial y)(e^{xy}sin(z))	\frac{\partial\:}{\partial\:y}(e^{xy}\sin(z))
limit as x approaches 1 of sqrt(x)	\lim\:_{x\to\:1}(\sqrt{x})
derivative of 4(x+4^{3/2})	\frac{d}{dx}(4(x+4)^{\frac{3}{2}})
integral of (1/x+e^x)	\int\:(\frac{1}{x}+e^{x})dx
y^{''}+64y=7tan(8x)	y^{\prime\:\prime\:}+64y=7\tan(8x)
limit as x approaches 0 of (x^5+9x)/x	\lim\:_{x\to\:0}(\frac{x^{5}+9x}{x})
derivative of e^{1+x^2}+3x^4	derivative\:e^{1+x^{2}}+3x^{4}
integral of (cos(2x))/(sin^7(2x))	\int\:\frac{\cos(2x)}{\sin^{7}(2x)}dx
(dy)/(dx)=x^3-2y	\frac{dy}{dx}=x^{3}-2y
tangent of y=3+4x^2-2x^3,(1,5)	tangent\:y=3+4x^{2}-2x^{3},(1,5)
derivative of f(x)=3x^2e^x+e^x(x^3+6)	derivative\:f(x)=3x^{2}e^{x}+e^{x}(x^{3}+6)
derivative of 7sec^2(7x)	\frac{d}{dx}(7\sec^{2}(7x))
derivative of x^{5/x}	\frac{d}{dx}(x^{\frac{5}{x}})
integral from 0 to 9 of xe^{-x^2}	\int\:_{0}^{9}xe^{-x^{2}}dx
taylor 1/(x^2),1	taylor\:\frac{1}{x^{2}},1
(\partial}{\partial x}(\frac{x^2)/y-xz)	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{y}-xz)
(\partial)/(\partial y)(2ln(3x)-4ln(2xy))	\frac{\partial\:}{\partial\:y}(2\ln(3x)-4\ln(2xy))
derivative of 3/(x^3)	derivative\:\frac{3}{x^{3}}
integral of 15x^4	\int\:15x^{4}dx
inverse oflaplace 3/(s^2-4)	inverselaplace\:\frac{3}{s^{2}-4}
derivative of x^{\sqrt[3]{ln(x}})	\frac{d}{dx}(x^{\sqrt[3]{\ln(x)}})
integral of-2/3 y^{-4/3}	\int\:-\frac{2}{3}y^{-\frac{4}{3}}dy
y=(3cos(x))/(1+sin(x))	y=\frac{3\cos(x)}{1+\sin(x)}
derivative of (tan(x)^{1/2})	\frac{d}{dx}((\tan(x))^{\frac{1}{2}})
integral from 0 to ln(3) of e^x	\int\:_{0}^{\ln(3)}e^{x}dx
integral of e^{cos(40t)}sin(40t)	\int\:e^{\cos(40t)}\sin(40t)dt
derivative of (6x/(x^2+36))	\frac{d}{dx}(\frac{6x}{x^{2}+36})
laplacetransform e^{-3}	laplacetransform\:e^{-3}
limit as t approaches 1+of t^{t/(1-t)}	\lim\:_{t\to\:1+}(t^{\frac{t}{1-t}})
derivative of (sin(x)/(tan(x)))	\frac{d}{dx}(\frac{\sin(x)}{\tan(x)})
limit as x approaches pi/5-of cot(5x)	\lim\:_{x\to\:\frac{π}{5}-}(\cot(5x))
derivative of (-2sin(2x)/(sqrt(13)))	\frac{d}{dx}(\frac{-2\sin(2x)}{\sqrt{13}})
integral of 1/(8^x)	\int\:\frac{1}{8^{x}}dx
tangent of f(x)=5x^2,\at x=0	tangent\:f(x)=5x^{2},\at\:x=0
sum from n=1 to infinity}(-1)^{n+1 of (n+1)/(2n^2+1)	\sum\:_{n=1}^{\infty\:}(-1)^{n+1}\frac{n+1}{2n^{2}+1}
integral of (ln(x^{7/2}))/x	\int\:\frac{\ln(x^{\frac{7}{2}})}{x}dx
derivative of (ln(x)^{{p}(x)})	\frac{d}{dx}((\ln(x))^{{p}(x)})
(dy)/(dx)= y/((x^2+1))	\frac{dy}{dx}=\frac{y}{(x^{2}+1)}
inverse oflaplace (16)/(s(s+2)^4)	inverselaplace\:\frac{16}{s(s+2)^{4}}
limit as x approaches infinity of (e^{-sx})/s	\lim\:_{x\to\:\infty\:}(\frac{e^{-sx}}{s})
(dy)/(dx)y=(8x^2-16+16)e^x	\frac{dy}{dx}y=(8x^{2}-16+16)e^{x}
derivative of (1+2x^2)(x-x^2)	derivative\:(1+2x^{2})(x-x^{2})
derivative of (x^3+8x)^3	derivative\:(x^{3}+8x)^{3}
integral from 0 to pi/2 of pisin^2(x)	\int\:_{0}^{\frac{π}{2}}π\sin^{2}(x)dx
integral of (1-cos(4x))/2	\int\:\frac{1-\cos(4x)}{2}dx
derivative of sqrt(7+\sqrt{7x)}	\frac{d}{dx}(\sqrt{7+\sqrt{7x}})
(\partial)/(\partial y)(4x-4y)	\frac{\partial\:}{\partial\:y}(4x-4y)
derivative of (4x^3/3+2x+cos(x)+1)	\frac{d}{dx}(\frac{4x^{3}}{3}+2x+\cos(x)+1)
derivative of (sqrt(2-x^2)^2)	\frac{d}{dx}((\sqrt{2-x^{2}})^{2})
tangent of y= 2/(x-2),(6, 2/5)	tangent\:y=\frac{2}{x-2},(6,\frac{2}{5})
(\partial)/(\partial x)((x-y)(1-xy))	\frac{\partial\:}{\partial\:x}((x-y)(1-xy))
derivative of ax^2+bx^2+c	\frac{d}{dx}(ax^{2}+bx^{2}+c)
integral of ln(x)sin(x)	\int\:\ln(x)\sin(x)dx
integral of 2/x-1/(x^2)	\int\:\frac{2}{x}-\frac{1}{x^{2}}dx
integral of (2x)/(sqrt(4x-5))	\int\:\frac{2x}{\sqrt{4x-5}}dx
(dr}{dt}=\frac{r^2)/t	\frac{dr}{dt}=\frac{r^{2}}{t}
derivative of (-3x+2)^2	derivative\:(-3x+2)^{2}
derivative of 5^{3x}+7	\frac{d}{dx}(5^{3x}+7)
derivative of ((x+7)/(x-7))^5	derivative\:(\frac{x+7}{x-7})^{5}
y^'+(3/(300-x))y=4	y^{\prime\:}+(\frac{3}{300-x})y=4
taylor f(x)=ln(1+x)	taylor\:f(x)=\ln(1+x)

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