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Popular Calculus Problems

(\partial)/(\partial x)(xyln(x^2+y^2))	\frac{\partial\:}{\partial\:x}(xy\ln(x^{2}+y^{2}))
derivative of ln(cosh(3x))	\frac{d}{dx}(\ln(\cosh(3x)))
limit as x approaches pi/4 of (sin(2x)-1)/(4x-pi)	\lim\:_{x\to\:\frac{π}{4}}(\frac{\sin(2x)-1}{4x-π})
derivative of cos(2x+3y)	\frac{d}{dx}(\cos(2x+3y))
y^{''}-16y^'+63y=240e^x	y^{\prime\:\prime\:}-16y^{\prime\:}+63y=240e^{x}
integral of (x-5)/(x^2+2x-3)	\int\:\frac{x-5}{x^{2}+2x-3}dx
tangent of f(x)= 3/(5x+2),\at x=-1	tangent\:f(x)=\frac{3}{5x+2},\at\:x=-1
area y=x,y=x^3	area\:y=x,y=x^{3}
integral of (2x+1)^{5/6}	\int\:(2x+1)^{\frac{5}{6}}dx
(\partial)/(\partial x)(32x+13y+90)	\frac{\partial\:}{\partial\:x}(32x+13y+90)
d/(dt)(ln(a+{v}(t)t))	\frac{d}{dt}(\ln(a+{v}(t)t))
derivative of (-1^nx^{2n})	\frac{d}{dx}((-1)^{n}x^{2n})
y^'=0.5y,y(2)=100	y^{\prime\:}=0.5y,y(2)=100
limit as x approaches-1 of (\|x+1\|)/(x+1)	\lim\:_{x\to\:-1}(\frac{\left\|x+1\right\|}{x+1})
integral from 1 to 2 of (2x+1)ln(x)	\int\:_{1}^{2}(2x+1)\ln(x)dx
integral of (x^2+1)/(x^3+3x-16)	\int\:\frac{x^{2}+1}{x^{3}+3x-16}dx
integral of sqrt(e^{2t)+e^{-2t}+2}	\int\:\sqrt{e^{2t}+e^{-2t}+2}dt
integral of xln(x^2+1)	\int\:x\ln(x^{2}+1)dx
inverse oflaplace 1/(s^2(s+1.1))	inverselaplace\:\frac{1}{s^{2}(s+1.1)}
integral of 1/(sqrt(2+x-x^2))	\int\:\frac{1}{\sqrt{2+x-x^{2}}}dx
integral of xsqrt(x^2-5)	\int\:x\sqrt{x^{2}-5}dx
limit as x approaches-1-of arccos(x)	\lim\:_{x\to\:-1-}(\arccos(x))
derivative of-xe^{-x}	\frac{d}{dx}(-xe^{-x})
derivative of 32x	\frac{d}{dx}(32x)
limit as x approaches 0+of 10xln(x)	\lim\:_{x\to\:0+}(10x\ln(x))
limit as x approaches 2-of (-3)/(x^2-4)	\lim\:_{x\to\:2-}(\frac{-3}{x^{2}-4})
laplacetransform 5e-3(t-2)	laplacetransform\:5e-3(t-2)
(\partial)/(\partial x)(3x^2y+2xy^2)	\frac{\partial\:}{\partial\:x}(3x^{2}y+2xy^{2})
limit as x approaches 3 of tan((3pi)/4)	\lim\:_{x\to\:3}(\tan(\frac{3π}{4}))
integral of 1/(2x+sqrt(x))	\int\:\frac{1}{2x+\sqrt{x}}dx
integral of re^{r/3}	\int\:re^{\frac{r}{3}}dr
(\partial)/(\partial x)(x^2+y^2-y^2x-2)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}-y^{2}x-2)
limit as x approaches infinity+of x^3	\lim\:_{x\to\:\infty\:+}(x^{3})
limit as x approaches 0-of 18-4/(x^3)	\lim\:_{x\to\:0-}(18-\frac{4}{x^{3}})
derivative of e^{xsinh(x})	\frac{d}{dx}(e^{x\sinh(x)})
limit as x approaches infinity of 2x+3	\lim\:_{x\to\:\infty\:}(2x+3)
integral of x/(\sqrt[3]{x^2-8)}	\int\:\frac{x}{\sqrt[3]{x^{2}-8}}dx
integral of 4/(sqrt(x^2+16))	\int\:\frac{4}{\sqrt{x^{2}+16}}dx
derivative of f(v)=(v^{-3}+6v^{-2})^3	derivative\:f(v)=(v^{-3}+6v^{-2})^{3}
tangent of f(x)= 3/(x+1)	tangent\:f(x)=\frac{3}{x+1}
(\partial)/(\partial z)(xycos(x+yz))	\frac{\partial\:}{\partial\:z}(xy\cos(x+yz))
(dy)/(dx)=20-5y	\frac{dy}{dx}=20-5y
integral of (2-8x)/(sqrt(1-4x^2))	\int\:\frac{2-8x}{\sqrt{1-4x^{2}}}dx
limit as x approaches 1 of 3x^3+2x^2+4	\lim\:_{x\to\:1}(3x^{3}+2x^{2}+4)
integral of (x^5)/(sqrt(1-x^2))	\int\:\frac{x^{5}}{\sqrt{1-x^{2}}}dx
derivative of 4^{x+1}	derivative\:4^{x+1}
limit as x approaches 1 of 2x^3-4x^2+x+7	\lim\:_{x\to\:1}(2x^{3}-4x^{2}+x+7)
(\partial)/(\partial x)(cos(2y))	\frac{\partial\:}{\partial\:x}(\cos(2y))
integral of sqrt(39-10x-x^2)	\int\:\sqrt{39-10x-x^{2}}dx
derivative of sqrt(18x-x^2)	\frac{d}{dx}(\sqrt{18x-x^{2}})
derivative of 4x+8	\frac{d}{dx}(4x+8)
derivative of f(x)=x-1/x	derivative\:f(x)=x-\frac{1}{x}
integral from 0 to 1 of x^5ln(x)	\int\:_{0}^{1}x^{5}\ln(x)dx
derivative of 3arctan(2x)	\frac{d}{dx}(3\arctan(2x))
integral of ((z^4+10z^3)/(2z^2))	\int\:(\frac{z^{4}+10z^{3}}{2z^{2}})dz
y^'-(2y)/x =x^2e^x	y^{\prime\:}-\frac{2y}{x}=x^{2}e^{x}
(\partial)/(\partial x)(e^{-kx^2})	\frac{\partial\:}{\partial\:x}(e^{-kx^{2}})
(dy)/(dx)=y(x^2+2)	\frac{dy}{dx}=y(x^{2}+2)
derivative of 8e^{-7x}	derivative\:8e^{-7x}
integral of 3sin^3(3xco)s^33x	\int\:3\sin^{3}(3xco)s^{3}3xdx
y^'=x^3	y^{\prime\:}=x^{3}
integral from 7 to 9 of (x^2+2x-8)	\int\:_{7}^{9}(x^{2}+2x-8)dx
(\partial)/(\partial x)(sin(8θ))	\frac{\partial\:}{\partial\:x}(\sin(8θ))
integral from 1 to infinity of e^{-9x}	\int\:_{1}^{\infty\:}e^{-9x}dx
integral of csc^2(y)	\int\:\csc^{2}(y)dy
(\partial)/(\partial x)(5x^{y/z})	\frac{\partial\:}{\partial\:x}(5x^{\frac{y}{z}})
xy^'=y+7x^2sin(x),y(pi)=0	xy^{\prime\:}=y+7x^{2}\sin(x),y(π)=0
limit as x approaches 1 of sqrt(5x+6)	\lim\:_{x\to\:1}(\sqrt{5x+6})
derivative of-3^{-2}(tan(7x)^5)	\frac{d}{dx}(-3^{-2}(\tan(7x))^{5})
(2cos(x))^'	(2\cos(x))^{\prime\:}
area y^2=x-2,y=x-4	area\:y^{2}=x-2,y=x-4
integral of (sec(2x)+tan(2x))	\int\:(\sec(2x)+\tan(2x))dx
derivative of f(x)=(2t+1)/(t+3)	derivative\:f(x)=\frac{2t+1}{t+3}
area y=2x^2+3,(0,3)	area\:y=2x^{2}+3,(0,3)
integral of (x^2+1)/(1-x^2)	\int\:\frac{x^{2}+1}{1-x^{2}}dx
limit as x approaches (5pi)/6 of sin(x)	\lim\:_{x\to\:\frac{5π}{6}}(\sin(x))
(dy)/(dx)=(xy)^2,y(0)=1	\frac{dy}{dx}=(xy)^{2},y(0)=1
integral of (x^5)/(x^6+2)	\int\:\frac{x^{5}}{x^{6}+2}dx
limit as x approaches 9 of 1/((x-9)^3)	\lim\:_{x\to\:9}(\frac{1}{(x-9)^{3}})
area 7cos(7x),7-7cos(7x)	area\:7\cos(7x),7-7\cos(7x)
integral of sec^9(x)tan(x)	\int\:\sec^{9}(x)\tan(x)dx
derivative of sin(pi*x)	\frac{d}{dx}(\sin(π\cdot\:x))
derivative of 7/(sqrt(x+8))	\frac{d}{dx}(\frac{7}{\sqrt{x+8}})
derivative of Ae^{-3x}	\frac{d}{dx}(Ae^{-3x})
integral of 1/(ln^2(x))	\int\:\frac{1}{\ln^{2}(x)}dx
area 2x^2+3,(-1,2)	area\:2x^{2}+3,(-1,2)
derivative of (1+cos^2(x)^6)	\frac{d}{dx}((1+\cos^{2}(x))^{6})
d/(dt)(15t^2)	\frac{d}{dt}(15t^{2})
derivative of x^8-x^{1/2}	derivative\:x^{8}-x^{\frac{1}{2}}
integral of (10x^2-9x+16)/(x^3+4x)	\int\:\frac{10x^{2}-9x+16}{x^{3}+4x}dx
-3y^'+(3y)/x =x^3y^4	-3y^{\prime\:}+\frac{3y}{x}=x^{3}y^{4}
(dy)/(dt)=2y+y^3,y(0)=1	\frac{dy}{dt}=2y+y^{3},y(0)=1
derivative of x^{2/7}	derivative\:x^{\frac{2}{7}}
derivative of 4x-3	derivative\:4x-3
tangent of y=(4x)/(1+x^2),(4, 16/17)	tangent\:y=\frac{4x}{1+x^{2}},(4,\frac{16}{17})
integral from 0 to pi/2 of-3sin^2(3x)	\int\:_{0}^{\frac{π}{2}}-3\sin^{2}(3x)dx
inverse oflaplace ((3-2s))/((s^2+4s+5))	inverselaplace\:\frac{(3-2s)}{(s^{2}+4s+5)}
integral of x^2-7x+5	\int\:x^{2}-7x+5dx
integral from 9/8 to 4 of 1/(1-x^2)	\int\:_{\frac{9}{8}}^{4}\frac{1}{1-x^{2}}dx
integral of-x/(1+x^2)	\int\:-\frac{x}{1+x^{2}}dx

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