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Popular Calculus Problems

integral of (3x^2)/(1+x^3)	\int\:\frac{3x^{2}}{1+x^{3}}dx
(\partial)/(\partial x)(sqrt(16-x^2-4y))	\frac{\partial\:}{\partial\:x}(\sqrt{16-x^{2}-4y})
limit as x approaches infinity of 2/(x!)	\lim\:_{x\to\:\infty\:}(\frac{2}{x!})
lcm ((csc^2(x)))/4 ,4sin^2(x)	lcm\:\frac{(\csc^{2}(x))}{4},4\sin^{2}(x)
(d^4)/(dx^4)(cos(x))	\frac{d^{4}}{dx^{4}}(\cos(x))
integral of sqrt(v)	\int\:\sqrt{v}dv
limit as x approaches 10 of sqrt(5)	\lim\:_{x\to\:10}(\sqrt{5})
y^'-5/x y=(y^5)/(x^5)	y^{\prime\:}-\frac{5}{x}y=\frac{y^{5}}{x^{5}}
limit as x approaches 0 of si	\lim\:_{x\to\:0}(si)
(dy)/(dx)=6+5x+36y+30xy	\frac{dy}{dx}=6+5x+36y+30xy
limit as x approaches 2-of (x^2+4)/(x-2)	\lim\:_{x\to\:2-}(\frac{x^{2}+4}{x-2})
integral of 4xe^x	\int\:4xe^{x}dx
limit as t approaches 0+of t+1	\lim\:_{t\to\:0+}(t+1)
integral of (x^2)/(cos^2(x))	\int\:\frac{x^{2}}{\cos^{2}(x)}dx
integral of 3v(v^2+6)^2	\int\:3v(v^{2}+6)^{2}dv
(\partial)/(\partial x)(4x^3y^3-4)	\frac{\partial\:}{\partial\:x}(4x^{3}y^{3}-4)
x^3dy+xydx=x^2dy+2ydx	x^{3}dy+xydx=x^{2}dy+2ydx
(\partial)/(\partial x)(ln((2x-1)/(x-1)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{2x-1}{x-1}))
(\partial)/(\partial y)((2x+y-4)e^{2y})	\frac{\partial\:}{\partial\:y}((2x+y-4)e^{2y})
integral of sin(t)cos(t)	\int\:\sin(t)\cos(t)dt
derivative of 2x^4sqrt(25-x^2)	derivative\:2x^{4}\sqrt{25-x^{2}}
y^{''''}+1=0	y^{\prime\:\prime\:\prime\:\prime\:}+1=0
(\partial)/(\partial x)(4/(xy)-x^2+3y^2)	\frac{\partial\:}{\partial\:x}(\frac{4}{xy}-x^{2}+3y^{2})
derivative of (1+x^2/((1-x^2)^2))	\frac{d}{dx}(\frac{1+x^{2}}{(1-x^{2})^{2}})
derivative of 5x^{7/4}+5x^{1/3}-2	derivative\:5x^{\frac{7}{4}}+5x^{\frac{1}{3}}-2
(2x+t)(dx)/(dt)+x-2t=0	(2x+t)\frac{dx}{dt}+x-2t=0
integral of e^{-x/b}	\int\:e^{-\frac{x}{b}}dx
integral of ((sqrt(x)-1)^2)/(sqrt(x))	\int\:\frac{(\sqrt{x}-1)^{2}}{\sqrt{x}}dx
derivative of 20x(1-x^3)	\frac{d}{dx}(20x(1-x)^{3})
integral of 1/((2x+5)^3)	\int\:\frac{1}{(2x+5)^{3}}dx
integral of sin(2x)x	\int\:\sin(2x)xdx
9x(dy)/(dx)=2xe^x-9y+6x^2	9x\frac{dy}{dx}=2xe^{x}-9y+6x^{2}
derivative of (2pi-x*cos(x)/(x-2pi))	\frac{d}{dx}(\frac{2π-x\cdot\:\cos(x)}{x-2π})
integral of (-2)(7x)	\int\:(-2)(7x)dx
integral of y^2cos(x)-3x^2y-2x	\int\:y^{2}\cos(x)-3x^{2}y-2xdx
(\partial)/(\partial x)(e^{-7x}cos(10x))	\frac{\partial\:}{\partial\:x}(e^{-7x}\cos(10x))
tangent of f(x)=10-4e^x,(0,6)	tangent\:f(x)=10-4e^{x},(0,6)
derivative of sin(4)	\frac{d}{dx}(\sin(4))
derivative of ln(x-1+1)	\frac{d}{dx}(\ln(x-1)+1)
limit as x approaches 2 of xln(x/(x-2))	\lim\:_{x\to\:2}(x\ln(\frac{x}{x-2}))
tangent of f(x)=4x^2+5x+17	tangent\:f(x)=4x^{2}+5x+17
derivative of 4x-6	\frac{d}{dx}(4x-6)
slope of (-1.2)(0)	slope\:(-1.2)(0)
integral of (5x^3+2x^2-6x+3)	\int\:(5x^{3}+2x^{2}-6x+3)dx
(dy)/(dt)-2ty=1	\frac{dy}{dt}-2ty=1
limit as x approaches 3-of 2x+1	\lim\:_{x\to\:3-}(2x+1)
area y=6x^4-6x^2,y=3x^2,x=0	area\:y=6x^{4}-6x^{2},y=3x^{2},x=0
(dy)/(dt)+e^ty=10e^t	\frac{dy}{dt}+e^{t}y=10e^{t}
integral of (x^2-x+5)/(x-1)	\int\:\frac{x^{2}-x+5}{x-1}dx
integral from 0 to pi/2 of xsin(6x)	\int\:_{0}^{\frac{π}{2}}x\sin(6x)dx
derivative of sqrt((x+\sqrt{x))}	derivative\:\sqrt{(x+\sqrt{x})}
limit as x approaches infinity of x^{12}	\lim\:_{x\to\:\infty\:}(x^{12})
integral of p(p+7)^7	\int\:p(p+7)^{7}dp
(\partial)/(\partial x)(y^6sin(6x))	\frac{\partial\:}{\partial\:x}(y^{6}\sin(6x))
integral of 1/(xsqrt(x^2+a^2))	\int\:\frac{1}{x\sqrt{x^{2}+a^{2}}}dx
y^'=x+9y	y^{\prime\:}=x+9y
derivative of x^3cos(x-x^3sin(x))	\frac{d}{dx}(x^{3}\cos(x)-x^{3}\sin(x))
limit as x approaches 2 of (x^2)/(2x-4)	\lim\:_{x\to\:2}(\frac{x^{2}}{2x-4})
(\partial)/(\partial x)((xy)/(x-y))	\frac{\partial\:}{\partial\:x}(\frac{xy}{x-y})
derivative of 450x-90x^2	\frac{d}{dx}(450x-90x^{2})
integral of-sin(y)	\int\:-\sin(y)dy
inverse oflaplace (2s+1)/(s(s+1))	inverselaplace\:\frac{2s+1}{s(s+1)}
limit as x approaches 0 of sqrt(x^3+x^2)	\lim\:_{x\to\:0}(\sqrt{x^{3}+x^{2}})
f(x)=3x*ln(x)	f(x)=3x\cdot\:\ln(x)
limit as n approaches infinity of 3n	\lim\:_{n\to\:\infty\:}(3n)
tangent of f(x)=sqrt(x+1),\at x=3	tangent\:f(x)=\sqrt{x+1},\at\:x=3
derivative of sin(3x^2+5)	derivative\:\sin(3x^{2}+5)
integral from 3 to 5 of x/8	\int\:_{3}^{5}\frac{x}{8}dx
(\partial)/(\partial x)((e^x+e^y)^8)	\frac{\partial\:}{\partial\:x}((e^{x}+e^{y})^{8})
integral of (e^u)/((6-e^u)^2)	\int\:\frac{e^{u}}{(6-e^{u})^{2}}du
integral of 4xsec(x)tan(x)	\int\:4x\sec(x)\tan(x)dx
(\partial)/(\partial x)(x^3y^5+2x^4y)	\frac{\partial\:}{\partial\:x}(x^{3}y^{5}+2x^{4}y)
derivative of-(9x)/y	derivative\:-\frac{9x}{y}
integral of (3x-1)^{-4}	\int\:(3x-1)^{-4}dx
y^'-7/(600+2t)y=6	y^{\prime\:}-\frac{7}{600+2t}y=6
integral from 0 to 2 of 1/(x^2)	\int\:_{0}^{2}\frac{1}{x^{2}}dx
(\partial)/(\partial x)(e^{xy}sin(xyz))	\frac{\partial\:}{\partial\:x}(e^{xy}\sin(xyz))
t^2y^{''}-7ty^'+15y=0	t^{2}y^{\prime\:\prime\:}-7ty^{\prime\:}+15y=0
inverse oflaplace (s^2)/(s^3-1)	inverselaplace\:\frac{s^{2}}{s^{3}-1}
integral of x(3x+2)	\int\:x(3x+2)dx
integral of xsinh(x)	\int\:x\sinh(x)dx
integral from 0 to 1 of 6(1+sqrt(x))^5	\int\:_{0}^{1}6(1+\sqrt{x})^{5}dx
derivative of (4x^2)	\frac{d}{dx}((4x)^{2})
(\partial)/(\partial z)(x^2+3yz+4xy)	\frac{\partial\:}{\partial\:z}(x^{2}+3yz+4xy)
sum from n=0 to infinity of 6(0.4)^n	\sum\:_{n=0}^{\infty\:}6(0.4)^{n}
derivative of ky(x^2)	\frac{d}{dx}(ky(x)^{2})
y^{''}-y=3e^x	y^{\prime\:\prime\:}-y=3e^{x}
derivative of (1/(x^2+3)(x^2-1/(x^2)+3))	\frac{d}{dx}((\frac{1}{x^{2}}+3)(x^{2}-\frac{1}{x^{2}}+3))
limit as n approaches infinity of ((-1)^{n+1})/(2n-1)	\lim\:_{n\to\:\infty\:}(\frac{(-1)^{n+1}}{2n-1})
integral from 0 to pi/2 of sin^5(xco)s^{12}x	\int\:_{0}^{\frac{π}{2}}\sin^{5}(xco)s^{12}x
(\partial)/(\partial x)(x^{1/2}*y^{1/2})	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{2}}\cdot\:y^{\frac{1}{2}})
derivative of e^{-x^2}+1	\frac{d}{dx}(e^{-x^{2}}+1)
(\partial)/(\partial x)(z^{x^y})	\frac{\partial\:}{\partial\:x}(z^{x^{y}})
tangent of f(x)= x/(x^2+81)	tangent\:f(x)=\frac{x}{x^{2}+81}
area x=2y^2-5,x=y^2+4	area\:x=2y^{2}-5,x=y^{2}+4
derivative of y=2x-5	derivative\:y=2x-5
integral of x^{-12}	\int\:x^{-12}dx
derivative of f(x)=6x^3-9x+4	derivative\:f(x)=6x^{3}-9x+4
tangent of (sqrt(x)+1)/(sqrt(x)+4)	tangent\:\frac{\sqrt{x}+1}{\sqrt{x}+4}
integral from 1 to 9 of (sqrt(x)-x)	\int\:_{1}^{9}(\sqrt{x}-x)dx

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