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Popular Calculus Problems

integral of e^{-x}cos(nx)	\int\:e^{-x}\cos(nx)dx
integral of sqrt(1+x/4)	\int\:\sqrt{1+\frac{x}{4}}dx
integral of ((x^2-1))/(sqrt(2x-1))	\int\:\frac{(x^{2}-1)}{\sqrt{2x-1}}dx
limit as x approaches 0 of 0/(x^2\|x\|)	\lim\:_{x\to\:0}(\frac{0}{x^{2}\left\|x\right\|})
(dy)/(dt)=t^2+20t^2y	\frac{dy}{dt}=t^{2}+20t^{2}y
integral of 1/(sqrt(9z^2-25))	\int\:\frac{1}{\sqrt{9z^{2}-25}}dz
derivative of y=2t(3t^2-5)^4	derivative\:y=2t(3t^{2}-5)^{4}
integral of e^{5x}cos(9x)	\int\:e^{5x}\cos(9x)dx
tangent of f(x)= 2/(sqrt(x)),\at x=9	tangent\:f(x)=\frac{2}{\sqrt{x}},\at\:x=9
(\partial)/(\partial z)(-1/((y+2z)^2))	\frac{\partial\:}{\partial\:z}(-\frac{1}{(y+2z)^{2}})
integral of (3e^{2x})/(1+e^{2x)}	\int\:\frac{3e^{2x}}{1+e^{2x}}dx
area f(x)=sin(2x),0, pi/2	area\:f(x)=\sin(2x),0,\frac{π}{2}
derivative of 5sin(x+3cos(x))	\frac{d}{dx}(5\sin(x)+3\cos(x))
derivative of e^{-xy}	\frac{d}{dx}(e^{-xy})
maclaurin ln(4+x)	maclaurin\:\ln(4+x)
limit as x approaches 0 of x(e^{1/x}-1)	\lim\:_{x\to\:0}(x(e^{\frac{1}{x}}-1))
derivative of e^{2sin(x})	\frac{d}{dx}(e^{2\sin(x)})
5x^2y^'=y^'+9xe^{-y}	5x^{2}y^{\prime\:}=y^{\prime\:}+9xe^{-y}
integral of ln(x)sqrt(x^7)	\int\:\ln(x)\sqrt{x^{7}}dx
derivative of y=-2x^4+7xe^x	derivative\:y=-2x^{4}+7xe^{x}
integral of 3picos^3(5pix)sin^7(5pix)	\int\:3π\cos^{3}(5πx)\sin^{7}(5πx)dx
derivative of 10t^4	derivative\:10t^{4}
(dy)/(dx)-(x+1)y=xy^2	\frac{dy}{dx}-(x+1)y=xy^{2}
7ty^'+y=0,y(1)=1	7ty^{\prime\:}+y=0,y(1)=1
integral of 5xsqrt(2x^2+3)	\int\:5x\sqrt{2x^{2}+3}dx
area y= 2/x ,y=8x,y= 1/(8x)	area\:y=\frac{2}{x},y=8x,y=\frac{1}{8x}
x(dy)/(dx)-y=sqrt(x^2+y^2)	x\frac{dy}{dx}-y=\sqrt{x^{2}+y^{2}}
derivative of f(x)=2xsqrt(2x^2+4)	derivative\:f(x)=2x\sqrt{2x^{2}+4}
integral of (x^2)/(\sqrt[3]{2x^3+9)}	\int\:\frac{x^{2}}{\sqrt[3]{2x^{3}+9}}dx
area 10x-5x^2,y=(10-5\sqrt[3]{4})x	area\:10x-5x^{2},y=(10-5\sqrt[3]{4})x
y^'=(3t+1)^2	y^{\prime\:}=(3t+1)^{2}
tangent of f(x)=(2x)/(-x+2)	tangent\:f(x)=\frac{2x}{-x+2}
(4du)/(dt)=u^2	\frac{4du}{dt}=u^{2}
integral of 1/(x(x^2+8)^2)	\int\:\frac{1}{x(x^{2}+8)^{2}}dx
limit as x approaches 3-of ax^2-bx+3	\lim\:_{x\to\:3-}(ax^{2}-bx+3)
inverse oflaplace 3t^2-5e^{3t}	inverselaplace\:3t^{2}-5e^{3t}
derivative of 1000^{log_{10}(x)}	derivative\:1000^{\log_{10}(x)}
integral of (x^2-4x+4)/(sqrt(x^2-4x+40))	\int\:\frac{x^{2}-4x+4}{\sqrt{x^{2}-4x+40}}dx
derivative of ln(ln(ln(x)))	derivative\:\ln(\ln(\ln(x)))
(d^3)/(dx^3)(9/x)	\frac{d^{3}}{dx^{3}}(\frac{9}{x})
2(d^2y)/(dx^2)+32y=0	2\frac{d^{2}y}{dx^{2}}+32y=0
integral of-1/(4x)	\int\:-\frac{1}{4x}dx
integral of (6x^3-x^2+2x-1)/(x^4+x^2)	\int\:\frac{6x^{3}-x^{2}+2x-1}{x^{4}+x^{2}}dx
derivative of e^{2x}+ln(2x)	\frac{d}{dx}(e^{2x}+\ln(2x))
integral of 3^x-5sin(2x)	\int\:3^{x}-5\sin(2x)dx
sum from n=0 to infinity of (n+1)^2	\sum\:_{n=0}^{\infty\:}(n+1)^{2}
(\partial)/(\partial x)((x^2+y)/(y^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}+y}{y^{2}})
y^{''}-4y^'+8y=0	y^{\prime\:\prime\:}-4y^{\prime\:}+8y=0
f(x)=arcsin(x/4)	f(x)=\arcsin(\frac{x}{4})
integral of x^{-1/6}	\int\:x^{-\frac{1}{6}}dx
integral from-2 to 2 of 1/(sqrt(4-x^2))	\int\:_{-2}^{2}\frac{1}{\sqrt{4-x^{2}}}dx
derivative of y=6x+10/3	derivative\:y=6x+\frac{10}{3}
derivative of 2x^{1/2}y^{1/2}	\frac{d}{dx}(2x^{\frac{1}{2}}y^{\frac{1}{2}})
derivative of 4/(cos(x)+1/(tan(x)))	\frac{d}{dx}(\frac{4}{\cos(x)}+\frac{1}{\tan(x)})
(\partial)/(\partial y)(3xsin(xy))	\frac{\partial\:}{\partial\:y}(3x\sin(xy))
y^{''}+y=sin(6t)	y^{\prime\:\prime\:}+y=\sin(6t)
tangent of y=x^4+2x^2-x,(1,2)	tangent\:y=x^{4}+2x^{2}-x,(1,2)
integral of 16xln(6x)	\int\:16x\ln(6x)dx
xy^'+y=8xy^2	xy^{\prime\:}+y=8xy^{2}
derivative of (4x+5)^{-1}	derivative\:(4x+5)^{-1}
sum from n=0 to infinity of 3/(4^n)	\sum\:_{n=0}^{\infty\:}\frac{3}{4^{n}}
derivative of x^2pi	\frac{d}{dx}(x^{2}π)
integral of ((sqrt(1+x^2)))/x	\int\:\frac{(\sqrt{1+x^{2}})}{x}dx
derivative of (3x)/(8-cot(x))	derivative\:\frac{3x}{8-\cot(x)}
derivative of f(x)=5^{-x/2}sin(2x)	derivative\:f(x)=5^{-\frac{x}{2}}\sin(2x)
limit as x approaches 0 of x^4+2e^x-2	\lim\:_{x\to\:0}(x^{4}+2e^{x}-2)
integral of ln(1+2^x)	\int\:\ln(1+2^{x})dx
integral from 1 to 3 of r^3ln(r)	\int\:_{1}^{3}r^{3}\ln(r)dr
derivative of (sqrt(2^2-x^2)/2)	\frac{d}{dx}(\frac{\sqrt{2^{2}-x^{2}}}{2})
tangent of 7x^2-x^3	tangent\:7x^{2}-x^{3}
derivative of (x-2)(4x+2)	derivative\:(x-2)(4x+2)
derivative of 4^{sin^2(x)+cos(3x)}	derivative\:4^{\sin^{2}(x)+\cos(3x)}
(1/t)^'	(\frac{1}{t})^{\prime\:}
(e^{x/2})^'	(e^{\frac{x}{2}})^{\prime\:}
limit as x approaches 2+of 6/(x-2)	\lim\:_{x\to\:2+}(\frac{6}{x-2})
integral of (28s^3)/(sqrt(8-s^4))	\int\:\frac{28s^{3}}{\sqrt{8-s^{4}}}ds
derivative of tan(pix)	derivative\:\tan(πx)
limit as x approaches 0 of (4x)/(sqrt(4+x)-\sqrt{4-x)}	\lim\:_{x\to\:0}(\frac{4x}{\sqrt{4+x}-\sqrt{4-x}})
integral of (2x-4)/(x^2+4)	\int\:\frac{2x-4}{x^{2}+4}dx
integral of (sqrt(x^2-25))	\int\:(\sqrt{x^{2}-25})dx
(\partial)/(\partial z)((x+y)/(z-3y))	\frac{\partial\:}{\partial\:z}(\frac{x+y}{z-3y})
(\partial)/(\partial x)(3(y+4)^3(x-2))	\frac{\partial\:}{\partial\:x}(3\cdot\:(y+4)^{3}\cdot\:(x-2))
integral from 1 to 5 of sqrt(x)	\int\:_{1}^{5}\sqrt{x}dx
derivative of 2sqrt(4-x^2)	\frac{d}{dx}(2\sqrt{4-x^{2}})
(\partial)/(\partial x)((4-z^2)/(3x))	\frac{\partial\:}{\partial\:x}(\frac{4-z^{2}}{3x})
integral of (x^2+3x-5)/(x-3)	\int\:\frac{x^{2}+3x-5}{x-3}dx
limit as x approaches 5+of (2-x)/(x-5)	\lim\:_{x\to\:5+}(\frac{2-x}{x-5})
integral of-4x(-6x^2-1)^6	\int\:-4x(-6x^{2}-1)^{6}dx
derivative of x^2-2/3 x^3	\frac{d}{dx}(x^{2}-\frac{2}{3}x^{3})
(\partial)/(\partial x)(sqrt(x)e^x)	\frac{\partial\:}{\partial\:x}(\sqrt{x}e^{x})
derivative of 2x^2e^{x/2}	\frac{d}{dx}(2x^{2}e^{\frac{x}{2}})
inverse oflaplace ((s-2))/(s^2-2s+10)	inverselaplace\:\frac{(s-2)}{s^{2}-2s+10}
limit as x approaches-5 of 1/(1+5)	\lim\:_{x\to\:-5}(\frac{1}{1+5})
derivative of (ln(x)^2sin(x))	\frac{d}{dx}((\ln(x))^{2}\sin(x))
(dy)/(dx)=(x-3)(y+1)^{2/3}	\frac{dy}{dx}=(x-3)(y+1)^{\frac{2}{3}}
integral of (4x)/((2x^2-8)^5)	\int\:\frac{4x}{(2x^{2}-8)^{5}}dx
derivative of (3/2 ^x)	\frac{d}{dx}((\frac{3}{2})^{x})
yy^'=t^2,y(0)=2	yy^{\prime\:}=t^{2},y(0)=2
y^'+3y=1,y(0)=1	y^{\prime\:}+3y=1,y(0)=1
implicit (dy)/(dx),xy=30	implicit\:\frac{dy}{dx},xy=30

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