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Popular Calculus Problems

integral of 1/(x^3+x)	\int\:\frac{1}{x^{3}+x}dx
derivative of 2^{x^2+3x}	\frac{d}{dx}(2^{x^{2}+3x})
integral of (x+5)cos(x)	\int\:(x+5)\cos(x)dx
integral of xcos^2(9x)	\int\:x\cos^{2}(9x)dx
(dy)/(dx)=4xe^y	\frac{dy}{dx}=4xe^{y}
derivative of (x^3+1(3-2x^3))	\frac{d}{dx}((x^{3}+1)(3-2x^{3}))
slope of (3,2),(5,6)	slope\:(3,2),(5,6)
area y=4x,y= 7/5 x,y=32-x^2	area\:y=4x,y=\frac{7}{5}x,y=32-x^{2}
derivative of (x-5xsqrt(x)/(sqrt(x)))	\frac{d}{dx}(\frac{x-5x\sqrt{x}}{\sqrt{x}})
derivative of xe^x-1	\frac{d}{dx}(xe^{x}-1)
tangent of f(x)=5x-4x^2,\at x=-1	tangent\:f(x)=5x-4x^{2},\at\:x=-1
integral from 0 to 3 of (2^x)	\int\:_{0}^{3}(2^{x})dx
y^{''}+2y^'+4y=50cos(x)	y^{\prime\:\prime\:}+2y^{\prime\:}+4y=50\cos(x)
integral of 2e^{2x}sin(e^{2x})	\int\:2e^{2x}\sin(e^{2x})dx
xy^'+y=-6xy^2	xy^{\prime\:}+y=-6xy^{2}
simplify 3/2 x^{2/3}	simplify\:\frac{3}{2}x^{\frac{2}{3}}
(\partial)/(\partial y)(aln(x^2+y^2))	\frac{\partial\:}{\partial\:y}(a\ln(x^{2}+y^{2}))
limit as x approaches 3-of 1/(6-2x)	\lim\:_{x\to\:3-}(\frac{1}{6-2x})
inverse oflaplace 1/(s^2-2s+5)	inverselaplace\:\frac{1}{s^{2}-2s+5}
derivative of (8+xf(x))/(sqrt(x))	derivative\:\frac{8+xf(x)}{\sqrt{x}}
tangent of x^2-2x+1	tangent\:x^{2}-2x+1
limit as x approaches 0+of 5/(x^2)	\lim\:_{x\to\:0+}(\frac{5}{x^{2}})
(x+y)^2dx+(2xy+x^2-8)dy=0	(x+y)^{2}dx+(2xy+x^{2}-8)dy=0
derivative of f(x)=3x^2+5x-1/(x^2)+e^2	derivative\:f(x)=3x^{2}+5x-\frac{1}{x^{2}}+e^{2}
limit as x approaches 0 of (3x+1)/(7x)	\lim\:_{x\to\:0}(\frac{3x+1}{7x})
tangent of x^3,\at x=2	tangent\:x^{3},\at\:x=2
integral of (x-1)^2x^3(2-x)	\int\:(x-1)^{2}\cdot\:x^{3}\cdot\:(2-x)dx
(dy)/(dx)=(5x)/(9y)	\frac{dy}{dx}=\frac{5x}{9y}
derivative of 7e^e	\frac{d}{dx}(7e^{e})
(\partial)/(\partial x)((x^3+y^2)^{1/2})	\frac{\partial\:}{\partial\:x}((x^{3}+y^{2})^{\frac{1}{2}})
y^{''}+2y^'+2y=1	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=1
derivative of (7-sec(x)/(tan(x)))	\frac{d}{dx}(\frac{7-\sec(x)}{\tan(x)})
limit as x approaches-infinity of x/(9-x^2)	\lim\:_{x\to\:-\infty\:}(\frac{x}{9-x^{2}})
x^2y^{''}+2xy^'-72y=0	x^{2}y^{\prime\:\prime\:}+2xy^{\prime\:}-72y=0
integral from 0 to 2 of (x+1)/(x(x^2+1))	\int\:_{0}^{2}\frac{x+1}{x(x^{2}+1)}dx
y^'=((x-ysin(2x)))/(sin^2(x))	y^{\prime\:}=\frac{(x-y\sin(2x))}{\sin^{2}(x)}
sum from n=1 to infinity of 1/(n*3^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{n\cdot\:3^{n}}
tangent of 3e^{-7x}	tangent\:3e^{-7x}
limit as x approaches-infinity of 3-x	\lim\:_{x\to\:-\infty\:}(3-x)
inverse oflaplace 4/(2s^2+2s+1)	inverselaplace\:\frac{4}{2s^{2}+2s+1}
derivative of y=e^4x^2+1	derivative\:y=e^{4}x^{2}+1
(\partial)/(\partial y)(3x^2y^2+1)	\frac{\partial\:}{\partial\:y}(3x^{2}y^{2}+1)
integral of x^{-1/2}(x^2-x+2)	\int\:x^{-\frac{1}{2}}(x^{2}-x+2)dx
x/((1+x^2))dx+y/((1+y^2))dy=0	\frac{x}{(1+x^{2})}dx+\frac{y}{(1+y^{2})}dy=0
f(x)=(2x)/(1+x^2)	f(x)=\frac{2x}{1+x^{2}}
63x^2y^{''}+14x(x-9)y^'-14(x-9)y=-2x^3	63x^{2}y^{\prime\:\prime\:}+14x(x-9)y^{\prime\:}-14(x-9)y=-2x^{3}
tangent of y=x^2-x	tangent\:y=x^{2}-x
limit as x approaches 0 of csc(0)	\lim\:_{x\to\:0}(\csc(0))
derivative of 5.7x+2.2	derivative\:5.7x+2.2
derivative of 5x^2+4x	\frac{d}{dx}(5x^{2}+4x)
derivative of 2^{10x}	\frac{d}{dx}(2^{10x})
integral of x^3sqrt(256-x^2)	\int\:x^{3}\sqrt{256-x^{2}}dx
derivative of cos(x/3 sin(x))	\frac{d}{dx}(\cos(\frac{x}{3})\sin(x))
integral of (tan(x))/(tan^2(x)+1)	\int\:\frac{\tan(x)}{\tan^{2}(x)+1}dx
integral of 8/(x^2sqrt(x^2+36))	\int\:\frac{8}{x^{2}\sqrt{x^{2}+36}}dx
d/(dt)(1/(2sqrt(t)))	\frac{d}{dt}(\frac{1}{2\sqrt{t}})
derivative of ln(x^{10})	derivative\:\ln(x^{10})
derivative of y=sqrt(3)x(x+2)^3	derivative\:y=\sqrt{3}x(x+2)^{3}
(\partial)/(\partial x)(-3x^2+3)	\frac{\partial\:}{\partial\:x}(-3x^{2}+3)
integral of-2cos(6x)	\int\:-2\cos(6x)dx
derivative of f(x)=8x^{15}-6x^3+1	derivative\:f(x)=8x^{15}-6x^{3}+1
(dy)/(dt)=y^2-y	\frac{dy}{dt}=y^{2}-y
area x^3-10x,15x	area\:x^{3}-10x,15x
y^{'''}+y^{''}-4y^'-4y=0	y^{\prime\:\prime\:\prime\:}+y^{\prime\:\prime\:}-4y^{\prime\:}-4y=0
integral from 0 to 6 of (6x+2)	\int\:_{0}^{6}(6x+2)dx
integral of \sqrt[-3]{x}+2x	\int\:\sqrt[-3]{x}+2xdx
derivative of (2x+1^{1/2})	\frac{d}{dx}((2x+1)^{\frac{1}{2}})
limit as x approaches 2 of F(x)	\lim\:_{x\to\:2}(F(x))
derivative of (6x^2+7(6x+sqrt(x)))	\frac{d}{dx}((6x^{2}+7)(6x+\sqrt{x}))
0=(x+y)dx+(x-y)dy	0=(x+y)dx+(x-y)dy
y^{''}+y=3sec^3(2t)	y^{\prime\:\prime\:}+y=3\sec^{3}(2t)
area x=y^2-4,x=4	area\:x=y^{2}-4,x=4
derivative of 1-2x^3	\frac{d}{dx}(1-2x^{3})
integral of e^xsin(nx)	\int\:e^{x}\sin(nx)dx
y^{''}+5y^'+6y=12	y^{\prime\:\prime\:}+5y^{\prime\:}+6y=12
derivative of f(x)=2x^3-5x^2+6	derivative\:f(x)=2x^{3}-5x^{2}+6
integral from-1 to 1 of x^2-2-e^x	\int\:_{-1}^{1}x^{2}-2-e^{x}dx
integral from 0 to pi of sin(t)	\int\:_{0}^{π}\sin(t)dt
y^'=2x-y	y^{\prime\:}=2x-y
derivative of 3^{x^2-x+5}	\frac{d}{dx}(3^{x^{2}-x+5})
derivative of (x^2+10x/((x+5)^2))	\frac{d}{dx}(\frac{x^{2}+10x}{(x+5)^{2}})
(\partial)/(\partial x)(4u(x,y))	\frac{\partial\:}{\partial\:x}(4u(x,y))
derivative of 1/(3x^2)	derivative\:\frac{1}{3x^{2}}
(\partial)/(\partial x)(x^2(1+2y))	\frac{\partial\:}{\partial\:x}(x^{2}(1+2y))
derivative of 1/2 x^2sqrt(36-x^2)	\frac{d}{dx}(\frac{1}{2}x^{2}\sqrt{36-x^{2}})
sum from n=0 to infinity of 2^n1^n	\sum\:_{n=0}^{\infty\:}2^{n}1^{n}
integral of 1/((x^2+1)^2)	\int\:\frac{1}{(x^{2}+1)^{2}}dx
integral of xcos^2(4x)	\int\:x\cos^{2}(4x)dx
derivative of 1/((x^2-1))	\frac{d}{dx}(\frac{1}{(x^{2}-1)})
-45y^{''}+35y^'=0,y(2)=2,y^'(-1)=-1	-45y^{\prime\:\prime\:}+35y^{\prime\:}=0,y(2)=2,y^{\prime\:}(-1)=-1
(x+e^y)dy-dx=0	(x+e^{y})dy-dx=0
integral of (3(2^x)-2(3^x))/(2^x)	\int\:\frac{3(2^{x})-2(3^{x})}{2^{x}}dx
derivative of x+9	\frac{d}{dx}(x+9)
limit as x approaches 5 of 3x^2-x-2	\lim\:_{x\to\:5}(3x^{2}-x-2)
xy^'+y=x^4y^4	xy^{\prime\:}+y=x^{4}y^{4}
(\partial)/(\partial x)(x^2+4x+y^2)	\frac{\partial\:}{\partial\:x}(x^{2}+4x+y^{2})
derivative of tan(e^{4t})+e^{tan(4t)}	derivative\:\tan(e^{4t})+e^{\tan(4t)}
x^{''}=-x	x^{\prime\:\prime\:}=-x
y=(2y^4+2x)y^'	y=(2y^{4}+2x)y^{\prime\:}
derivative of (e^{2x})/(sin(3x))	derivative\:\frac{e^{2x}}{\sin(3x)}

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