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Popular Calculus Problems

integral of 8/((t^2+1)^{3/2)}	\int\:\frac{8}{(t^{2}+1)^{\frac{3}{2}}}dt
integral from-2 to 1 of x^3	\int\:_{-2}^{1}x^{3}dx
derivative of 2/(t^2)	derivative\:\frac{2}{t^{2}}
area sin(x),cos(x),0, pi/2	area\:\sin(x),\cos(x),0,\frac{π}{2}
(x-1)y^'-2+3x+y=0	(x-1)y^{\prime\:}-2+3x+y=0
integral from 0 to 1 of 1/(e^x+e^{-x)}	\int\:_{0}^{1}\frac{1}{e^{x}+e^{-x}}dx
derivative of-3ln(3+4x^2+5x^3-9)	\frac{d}{dx}(-3\ln(3+4x^{2})+5x^{3}-9)
derivative of y=6	derivative\:y=6
t^2(dy)/(dt)-t=1+y+ty,y(1)=10	t^{2}\frac{dy}{dt}-t=1+y+ty,y(1)=10
derivative of 6x^6	\frac{d}{dx}(6x^{6})
integral from-35 to 0 of 1/(sqrt(1-x))	\int\:_{-35}^{0}\frac{1}{\sqrt{1-x}}dx
integral of 2x^2e^{x^2}	\int\:2x^{2}e^{x^{2}}dx
integral of (14)/x	\int\:\frac{14}{x}dx
derivative of f(x)=x^2*(x^3+2)	derivative\:f(x)=x^{2}\cdot\:(x^{3}+2)
(dy)/(dx)=(16sqrt(x))/(e^y)	\frac{dy}{dx}=\frac{16\sqrt{x}}{e^{y}}
y^{''}+4y=12sin(2x)	y^{\prime\:\prime\:}+4y=12\sin(2x)
derivative of f(x)= 4/(3x^2)+1/(x^{2.1)}	derivative\:f(x)=\frac{4}{3x^{2}}+\frac{1}{x^{2.1}}
integral of ((8+x+x^2))/(sqrt(x))	\int\:\frac{(8+x+x^{2})}{\sqrt{x}}dx
limit as x approaches 4-of (6x)/(x-4)	\lim\:_{x\to\:4-}(\frac{6x}{x-4})
f(x)=3sin^2(x)	f(x)=3\sin^{2}(x)
2y^{''}+y^'-2y=0	2y^{\prime\:\prime\:}+y^{\prime\:}-2y=0
limit as x approaches 5 of cos(x)	\lim\:_{x\to\:5}(\cos(x))
derivative of y=2x^{3pi}	derivative\:y=2x^{3π}
(5t+3y+3)dt-dy=0	(5t+3y+3)dt-dy=0
derivative of x^3-4x^2+5	\frac{d}{dx}(x^{3}-4x^{2}+5)
derivative of xsqrt(x)\sqrt[3]{x}	\frac{d}{dx}(x\sqrt{x}\sqrt[3]{x})
(dy)/(dx)+y^7x+7y=0	\frac{dy}{dx}+y^{7}x+7y=0
(\partial)/(\partial y)(x^2z^2sin(4y))	\frac{\partial\:}{\partial\:y}(x^{2}z^{2}\sin(4y))
integral of (xcos(3x))	\int\:(x\cos(3x))dx
limit as x approaches-2 of (2x^3+9x^2+12x+4)/(-x^3-2x^2+4x+8)	\lim\:_{x\to\:-2}(\frac{2x^{3}+9x^{2}+12x+4}{-x^{3}-2x^{2}+4x+8})
integral of-x^{3/2}	\int\:-x^{\frac{3}{2}}dx
integral from-1 to 1 of (x^3-x)	\int\:_{-1}^{1}(x^{3}-x)dx
integral from 0 to c of 9e^{3x}	\int\:_{0}^{c}9e^{3x}dx
(\partial)/(\partial x)(3sin(2xy))	\frac{\partial\:}{\partial\:x}(3\sin(2xy))
limit as x approaches infinity of e^{8x}	\lim\:_{x\to\:\infty\:}(e^{8x})
derivative of (2x^3+9x^5)	\frac{d}{dx}((2x^{3}+9x)^{5})
integral of 12x^2-5x+4	\int\:12x^{2}-5x+4dx
integral from-2 to 2 of 1/(x^2+4)	\int\:_{-2}^{2}\frac{1}{x^{2}+4}dx
derivative of e^{2x+5}+1/(e^{x^2})	\frac{d}{dx}(e^{2x+5}+\frac{1}{e^{x^{2}}})
(\partial)/(\partial x)(7xcos(5xy))	\frac{\partial\:}{\partial\:x}(7x\cos(5xy))
xyy^'=4x^2+2y^2	xyy^{\prime\:}=4x^{2}+2y^{2}
derivative of x*y^2	\frac{d}{dx}(x\cdot\:y^{2})
laplacetransform t^{5/2}	laplacetransform\:t^{\frac{5}{2}}
integral of x^4e^{(x^5)}	\int\:x^{4}e^{(x^{5})}dx
limit as x approaches 5 of (x^2+1)/(x-5)	\lim\:_{x\to\:5}(\frac{x^{2}+1}{x-5})
inverse oflaplace 1/(s^2-2s+3)	inverselaplace\:\frac{1}{s^{2}-2s+3}
(\partial)/(\partial x)(3x^2-2x+6y^2+2y+2)	\frac{\partial\:}{\partial\:x}(3x^{2}-2x+6y^{2}+2y+2)
integral of (u^4-u^3+u^2)	\int\:(u^{4}-u^{3}+u^{2})du
(\partial)/(\partial x)(4y-2xy)	\frac{\partial\:}{\partial\:x}(4y-2xy)
derivative of sqrt(sin(2x))	derivative\:\sqrt{\sin(2x)}
limit as x approaches 2 of 1/((x-2))	\lim\:_{x\to\:2}(\frac{1}{(x-2)})
integral of (2x^3+x^2-7x+7)/(x^2+x-2)	\int\:\frac{2x^{3}+x^{2}-7x+7}{x^{2}+x-2}dx
(\partial)/(\partial y)(xye^{4y})	\frac{\partial\:}{\partial\:y}(xye^{4y})
integral from 1 to 4 of sqrt(1+9/4 x)	\int\:_{1}^{4}\sqrt{1+\frac{9}{4}x}dx
derivative of x/(1-2x^2)	\frac{d}{dx}(\frac{x}{1-2x^{2}})
integral of ((3x+2))/(x(x+1)^2)	\int\:\frac{(3x+2)}{x(x+1)^{2}}dx
derivative of 2e^{-x}	derivative\:2e^{-x}
integral of (sec^2(x))/(tan^3(x))	\int\:\frac{\sec^{2}(x)}{\tan^{3}(x)}dx
6t(dy)/(dt)+y=sqrt(t)	6t\frac{dy}{dt}+y=\sqrt{t}
derivative of 3x^2-3	derivative\:3x^{2}-3
derivative of x^5sin(x)	derivative\:x^{5}\sin(x)
limit as x approaches 0 of (1-cos^2(3x))/(x^2)	\lim\:_{x\to\:0}(\frac{1-\cos^{2}(3x)}{x^{2}})
derivative of f(x)=3arcsin(x^4)	derivative\:f(x)=3\arcsin(x^{4})
integral from 0 to 1 of 3x^2	\int\:_{0}^{1}3x^{2}dx
limit as x approaches-2 of (4-x^2)/(x+2)	\lim\:_{x\to\:-2}(\frac{4-x^{2}}{x+2})
integral of 10sinh(4x-ln(2))	\int\:10\sinh(4x-\ln(2))dx
integral of ln(x)x	\int\:\ln(x)xdx
derivative of (xln(x)^2)	\frac{d}{dx}((x\ln(x))^{2})
(\partial)/(\partial x)(sqrt(x^2+2xy+y^4))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+2xy+y^{4}})
tangent of f(x)= 4/x ,(-9,-4/9)	tangent\:f(x)=\frac{4}{x},(-9,-\frac{4}{9})
(\partial)/(\partial y)(x+y-8)	\frac{\partial\:}{\partial\:y}(x+y-8)
integral from 0 to 8 of 1/(\sqrt[3]{x)}	\int\:_{0}^{8}\frac{1}{\sqrt[3]{x}}dx
(\partial)/(\partial x)(e^{x^2}+2y^3)	\frac{\partial\:}{\partial\:x}(e^{x^{2}}+2y^{3})
integral of (x+1)ln(x)	\int\:(x+1)\ln(x)dx
tangent of f(x)=x^2sqrt(x^3+1)	tangent\:f(x)=x^{2}\sqrt{x^{3}+1}
integral of x*f(x)	\int\:x\cdot\:f(x)dx
derivative of 2y^2+3x	\frac{d}{dx}(2y^{2}+3x)
(\partial)/(\partial y)(x^3-6xy+8y^3)	\frac{\partial\:}{\partial\:y}(x^{3}-6xy+8y^{3})
(\partial)/(\partial x)(cos(7x+4y+z))	\frac{\partial\:}{\partial\:x}(\cos(7x+4y+z))
limit as x approaches 0 of (ln(1-3x))/x	\lim\:_{x\to\:0}(\frac{\ln(1-3x)}{x})
integral of 15x^2-cos(x)+Cx+C	\int\:15x^{2}-\cos(x)+Cx+Cdx
derivative of f(x)=((x^2-4x))/(x+1)	derivative\:f(x)=\frac{(x^{2}-4x)}{x+1}
limit as x approaches 0+of ln(7/(x^5))	\lim\:_{x\to\:0+}(\ln(\frac{7}{x^{5}}))
15y^{''}+7y^'-2y=0	15y^{\prime\:\prime\:}+7y^{\prime\:}-2y=0
integral of sin(pix)cos(pix)	\int\:\sin(πx)\cos(πx)dx
derivative of cosh(ax)	\frac{d}{dx}(\cosh(ax))
derivative of \sqrt[3]{t}+2sqrt(t^3)	derivative\:\sqrt[3]{t}+2\sqrt{t^{3}}
integral of (2x^2+x+2)/((x^2+1)^2)	\int\:\frac{2x^{2}+x+2}{(x^{2}+1)^{2}}dx
integral of \sqrt[12]{x}+\sqrt[13]{x}	\int\:\sqrt[12]{x}+\sqrt[13]{x}dx
(\partial)/(\partial x)((2*x)/(x^2-y^2))	\frac{\partial\:}{\partial\:x}(\frac{2\cdot\:x}{x^{2}-y^{2}})
d/(d{z)}(({y})/({z)})	\frac{d}{d{z}}(\frac{{y}}{{z}})
derivative of ((x+1/(x-1))^3)	\frac{d}{dx}((\frac{x+1}{x-1})^{3})
integral of ysqrt(4+4y-4y^2)	\int\:y\sqrt{4+4y-4y^{2}}dy
(\partial)/(\partial x)(y^8+4x^3y^3)	\frac{\partial\:}{\partial\:x}(y^{8}+4x^{3}y^{3})
derivative of [x^2(x^2+6x)]^6	derivative\:[x^{2}(x^{2}+6x)]^{6}
integral of ((x^2-x+12))/(x^3+3x)	\int\:\frac{(x^{2}-x+12)}{x^{3}+3x}dx
derivative of 4v^2-2	derivative\:4v^{2}-2
limit as x approaches 0 of 1/x sin(1/x)	\lim\:_{x\to\:0}(\frac{1}{x}\sin(\frac{1}{x}))
integral of 18cos^2(x)sin(x)	\int\:18\cos^{2}(x)\sin(x)dx
limit as x approaches 0 of (3-5x)/(4x)	\lim\:_{x\to\:0}(\frac{3-5x}{4x})

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