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Popular Calculus Problems

y^{''}+529y=sec(23x)	y^{\prime\:\prime\:}+529y=\sec(23x)
derivative of 2cos(-6x)	\frac{d}{dx}(2\cos(-6x))
integral from 0 to pi of cos^4(x)	\int\:_{0}^{π}\cos^{4}(x)dx
derivative of 1-sin(xcos(x))	\frac{d}{dx}(1-\sin(x)\cos(x))
integral of tcsc^2((3t^2)/2)	\int\:t\csc^{2}(\frac{3t^{2}}{2})dt
sum from n=4 to infinity of 1/(n^2)	\sum\:_{n=4}^{\infty\:}\frac{1}{n^{2}}
tangent of f(x)= 6/(5x+2),(-1,-2)	tangent\:f(x)=\frac{6}{5x+2},(-1,-2)
integral of ((sin(4x))/4)-((sin^3(x))/4)	\int\:(\frac{\sin(4x)}{4})-(\frac{\sin^{3}(x)}{4})dx
sum from n=0 to infinity of n(n+1)-1	\sum\:_{n=0}^{\infty\:}n(n+1)-1
integral of cos(x+pi)	\int\:\cos(x+π)dx
inverse oflaplace (e^{-s})/(s^2(s+2))	inverselaplace\:\frac{e^{-s}}{s^{2}(s+2)}
integral of 1+e^{2x}	\int\:1+e^{2x}dx
derivative of 25x^2e^{2x}-16	\frac{d}{dx}(25x^{2}e^{2x}-16)
area 0,x^2,x+2	area\:0,x^{2},x+2
inverse oflaplace (-8)/(s(s+2))	inverselaplace\:\frac{-8}{s(s+2)}
sum from n=1 to infinity of 1/(3(n^3+4))	\sum\:_{n=1}^{\infty\:}\frac{1}{3(n^{3}+4)}
sum from n=1 to infinity of n^2(1/3)^n	\sum\:_{n=1}^{\infty\:}n^{2}(\frac{1}{3})^{n}
integral of 1-x/(sqrt(y-x^2))	\int\:1-\frac{x}{\sqrt{y-x^{2}}}
(dy)/(dx)= 1/10y(500-y)	\frac{dy}{dx}=\frac{1}{10}\cdot\:y\cdot\:(500-y)
derivative of sin^2(x+5)	\frac{d}{dx}(\sin^{2}(x+5))
derivative of (e^3^{x-1})	\frac{d}{dx}((e^{3})^{x-1})
derivative of 5x^8	\frac{d}{dx}(5x^{8})
integral of ((1-tcos(t)))/t	\int\:\frac{(1-t\cos(t))}{t}dt
inverse oflaplace 5/(s+1)	inverselaplace\:\frac{5}{s+1}
area 4x^4-4x^2,3x^2,[0,0]	area\:4x^{4}-4x^{2},3x^{2},[0,0]
sum from n=1 to infinity of cos^n(1.6)	\sum\:_{n=1}^{\infty\:}\cos^{n}(1.6)
derivative of e^xx^2	\frac{d}{dx}(e^{x}x^{2})
integral of (5x^2+7x+11)	\int\:(5x^{2}+7x+11)dx
integral from 0 to 1/2 of xcos(pix)	\int\:_{0}^{\frac{1}{2}}x\cos(πx)dx
(\partial)/(\partial x)(cos^6(x^9y^8))	\frac{\partial\:}{\partial\:x}(\cos^{6}(x^{9}y^{8}))
(\partial)/(\partial x)(ln(x^4+y^9))	\frac{\partial\:}{\partial\:x}(\ln(x^{4}+y^{9}))
(\partial)/(\partial x)(x*e^{-y})	\frac{\partial\:}{\partial\:x}(x\cdot\:e^{-y})
(dy)/(dx)=1	\frac{dy}{dx}=1
integral of ((sqrt(x)+1)^4)/(2sqrt(x))	\int\:\frac{(\sqrt{x}+1)^{4}}{2\sqrt{x}}dx
derivative of x^2sin(4x-3)	\frac{d}{dx}(x^{2}\sin(4x-3))
limit as x approaches-2 of (3x+6)/(x+2)	\lim\:_{x\to\:-2}(\frac{3x+6}{x+2})
integral of (1+e)^5	\int\:(1+e)^{5}dx
integral from 1 to 16 of 1/(3-sqrt(x))	\int\:_{1}^{16}\frac{1}{3-\sqrt{x}}dx
4t*(dy)/(dt)-y=sqrt(t)	4t\cdot\:\frac{dy}{dt}-y=\sqrt{t}
limit as x approaches 0 of tan(5x)	\lim\:_{x\to\:0}(\tan(5x))
limit as x approaches 1-of 3x-1	\lim\:_{x\to\:1-}(3x-1)
area y=x^2-x^3,(0,1)	area\:y=x^{2}-x^{3},(0,1)
(\partial)/(\partial x)(sec^2(x))	\frac{\partial\:}{\partial\:x}(\sec^{2}(x))
(\partial)/(\partial x)(-2e^{2y}sin(2x))	\frac{\partial\:}{\partial\:x}(-2e^{2y}\sin(2x))
(\partial)/(\partial x)(e^{-y}+x^2)	\frac{\partial\:}{\partial\:x}(e^{-y}+x^{2})
derivative of {f}(x(-x))	\frac{d}{dx}({f}(x)(-x))
derivative of 20x^{7/5}-6x^{2/13}	derivative\:20x^{\frac{7}{5}}-6x^{\frac{2}{13}}
tangent of x^5	tangent\:x^{5}
integral of csc^2(x/3)	\int\:\csc^{2}(\frac{x}{3})dx
(\partial)/(\partial y)(5y^2e^{5xy})	\frac{\partial\:}{\partial\:y}(5y^{2}e^{5xy})
integral of sin(wt)	\int\:\sin(wt)dt
xy^'= 1/(y^3)	xy^{\prime\:}=\frac{1}{y^{3}}
integral from-1 to 2 of (-x^2+x+2)^2	\int\:_{-1}^{2}(-x^{2}+x+2)^{2}dx
limit as x approaches infinity of x/0	\lim\:_{x\to\:\infty\:}(\frac{x}{0})
integral of (5x\sqrt[3]{5x^2+1})/3	\int\:\frac{5x\sqrt[3]{5x^{2}+1}}{3}dx
derivative of-cos^2(x)	derivative\:-\cos^{2}(x)
derivative of 8/(x-2)	derivative\:\frac{8}{x-2}
integral of 6sin(3x)-cos(2x)	\int\:6\sin(3x)-\cos(2x)dx
derivative of ln(sin(x^2+1))	\frac{d}{dx}(\ln(\sin(x^{2})+1))
integral of 4x^6-2x^3+7x-4	\int\:4x^{6}-2x^{3}+7x-4dx
integral from 2 to 5 of 1/(x^2)	\int\:_{2}^{5}\frac{1}{x^{2}}dx
integral from 0 to 2 of ((4x+3))/(x^4)	\int\:_{0}^{2}\frac{(4x+3)}{x^{4}}dx
derivative of asin^3(x/3)	\frac{d}{dx}(a\sin^{3}(\frac{x}{3}))
y^'+y/x =(e^x)/x	y^{\prime\:}+\frac{y}{x}=\frac{e^{x}}{x}
tangent of sqrt(5x+4),\at x=9	tangent\:\sqrt{5x+4},\at\:x=9
limit as x approaches-2 of sqrt(4x^2)-3	\lim\:_{x\to\:-2}(\sqrt{4x^{2}}-3)
f(x)=2-x^2	f(x)=2-x^{2}
limit as x approaches 1 of f(x)(x^2-2x)	\lim\:_{x\to\:1}(f(x)(x^{2}-2x))
derivative of 3x-ln(3x+1)	\frac{d}{dx}(3x-\ln(3x+1))
area 2sqrt(x),x	area\:2\sqrt{x},x
limit as x approaches 0 of 6	\lim\:_{x\to\:0}(6)
derivative of 10-10e^{-2x}	\frac{d}{dx}(10-10e^{-2x})
limit as x approaches 1+of 1/(x+1)	\lim\:_{x\to\:1+}(\frac{1}{x+1})
derivative of x^2sin^8(x)+xcos^{-5}(x)	derivative\:x^{2}\sin^{8}(x)+x\cos^{-5}(x)
derivative of 1/3 (e^{3-x})	\frac{d}{dx}(\frac{1}{3}(e^{3-x}))
(\partial)/(\partial x)((3x-3z)/(2y+3z))	\frac{\partial\:}{\partial\:x}(\frac{3x-3z}{2y+3z})
sum from n=0 to infinity of sqrt(n+1)	\sum\:_{n=0}^{\infty\:}\sqrt{n+1}
integral of (6x^2-6x+2)	\int\:(6x^{2}-6x+2)dx
derivative of (e^x)/(7+e^x)	derivative\:\frac{e^{x}}{7+e^{x}}
(d^2)/(dx^2)(1/(x-1))	\frac{d^{2}}{dx^{2}}(\frac{1}{x-1})
integral of+x^6ln(x)	\int\:+x^{6}\ln(x)dx
derivative of (y^4)/(x^{12)}+8e^x	derivative\:\frac{y^{4}}{x^{12}}+8e^{x}
integral from 0 to 5 of (xe^{-x})	\int\:_{0}^{5}(xe^{-x})dx
derivative of 2+xsqrt(x)	\frac{d}{dx}(2+x\sqrt{x})
derivative of y=(x^5+1)^7	derivative\:y=(x^{5}+1)^{7}
(dy)/(dx)-y=2e^xy^2	\frac{dy}{dx}-y=2e^{x}y^{2}
integral of t*sin(t)	\int\:t\cdot\:\sin(t)dt
inverse oflaplace 1/((s+1)^4)	inverselaplace\:\frac{1}{(s+1)^{4}}
(\partial)/(\partial x)(ye^{6x})	\frac{\partial\:}{\partial\:x}(ye^{6x})
derivative of f(x)=(3)e^{-5x}	derivative\:f(x)=(3)e^{-5x}
integral from 0 to 2 of 4t^7	\int\:_{0}^{2}4t^{7}dt
integral of ((x^2-1)/(x^{3/2)})	\int\:(\frac{x^{2}-1}{x^{\frac{3}{2}}})dx
limit as x approaches 0 of (5^x-10^x)/x	\lim\:_{x\to\:0}(\frac{5^{x}-10^{x}}{x})
limit as x approaches 5 of sqrt(x^3+2x)	\lim\:_{x\to\:5}(\sqrt{x^{3}+2x})
integral of 1/(2(x^3+x^2))	\int\:\frac{1}{2(x^{3}+x^{2})}dx
y^{1/2}(dy)/(dx)+y^{3/2}=1,y(0)=9	y^{\frac{1}{2}}\frac{dy}{dx}+y^{\frac{3}{2}}=1,y(0)=9
derivative of 17e^x-ex^e	derivative\:17e^{x}-ex^{e}
(\partial)/(\partial x)(e^{-x}sin(yz))	\frac{\partial\:}{\partial\:x}(e^{-x}\sin(yz))
tangent of f(x)=2x^5-6x^3,\at x=1	tangent\:f(x)=2x^{5}-6x^{3},\at\:x=1
integral of ln(x	\int\:\ln(d)xdx

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