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Popular Calculus Problems

integral of sec^6(x)tan^6(x)	\int\:\sec^{6}(x)\tan^{6}(x)dx
tangent of ln(x^4+3)	tangent\:\ln(x^{4}+3)
integral from 0 to 1 of 2pi(x)(e^{-x^2})	\int\:_{0}^{1}2π(x)(e^{-x^{2}})dx
derivative of (3-x)^2	derivative\:(3-x)^{2}
derivative of e^x-cot(x)	derivative\:e^{x}-\cot(x)
inverse oflaplace 1/((s(s^2+s+1)))	inverselaplace\:\frac{1}{(s(s^{2}+s+1))}
integral of 1/(4e^{-2x)+e^{2x}}	\int\:\frac{1}{4e^{-2x}+e^{2x}}dx
(dy)/(dx)=((x^3+2y^3))/(xy^2)	\frac{dy}{dx}=\frac{(x^{3}+2y^{3})}{xy^{2}}
taylor x^{(1/2)}	taylor\:x^{(\frac{1}{2})}
limit as x approaches 0+of 2x-1	\lim\:_{x\to\:0+}(2x-1)
derivative of nln(1/x)	\frac{d}{dx}(n\ln(\frac{1}{x}))
(\partial)/(\partial x)((47x^2)/((x-y)^2))	\frac{\partial\:}{\partial\:x}(\frac{47x^{2}}{(x-y)^{2}})
integral of x/(sqrt(x^2+y^2))	\int\:\frac{x}{\sqrt{x^{2}+y^{2}}}dx
limit as x approaches 0+of 0^x	\lim\:_{x\to\:0+}(0^{x})
y^'=y(xy^5+5)	y^{\prime\:}=y(xy^{5}+5)
integral of sec^4(x)tan^6(x)	\int\:\sec^{4}(x)\tan^{6}(x)dx
t^2((dy)/(dt))+y=0	t^{2}(\frac{dy}{dt})+y=0
(\partial)/(\partial y)(ye^z)	\frac{\partial\:}{\partial\:y}(ye^{z})
(dy)/(dx)+xy=xy^{-3}	\frac{dy}{dx}+xy=xy^{-3}
limit as x approaches-4pi of 1+csc(x)	\lim\:_{x\to\:-4π}(1+\csc(x))
area x^2-6x,-x^2+2x	area\:x^{2}-6x,-x^{2}+2x
derivative of y=x-6	derivative\:y=x-6
integral of 5x^4-7x^6-3x^2	\int\:5x^{4}-7x^{6}-3x^{2}dx
(\partial}{\partial u}(\frac{v+u)/2)	\frac{\partial\:}{\partial\:u}(\frac{v+u}{2})
derivative of 3x^3y	\frac{d}{dx}(3x^{3}y)
integral from 0 to 3 of 1/(sqrt(x))	\int\:_{0}^{3}\frac{1}{\sqrt{x}}dx
integral from 0 to t of xe^{-x}	\int\:_{0}^{t}xe^{-x}dx
xy^'-y=2x^2-2x-2	xy^{\prime\:}-y=2x^{2}-2x-2
xy^'-y=x,y(1)=10	xy^{\prime\:}-y=x,y(1)=10
integral from 0 to 2 of pi(3x^2)^2	\int\:_{0}^{2}π(3x^{2})^{2}dx
(\partial)/(\partial x)(4x^2+3y^4)	\frac{\partial\:}{\partial\:x}(4x^{2}+3y^{4})
limit as x approaches 1-of 1/x-1	\lim\:_{x\to\:1-}(\frac{1}{x}-1)
y^{''}+9y=3sec(3t)	y^{\prime\:\prime\:}+9y=3\sec(3t)
f(x)=cos(x^2)*2x	f(x)=\cos(x^{2})\cdot\:2x
area y=x+1,y=9-x^2,x=-1,x=2	area\:y=x+1,y=9-x^{2},x=-1,x=2
integral of (sin^4(x)cos^2(x))	\int\:(\sin^{4}(x)\cos^{2}(x))dx
integral of (4x^2+3x+4)/((x^2+1)^2)	\int\:\frac{4x^{2}+3x+4}{(x^{2}+1)^{2}}dx
integral from-1 to 0 of (30e^{1/x})/(x^3)	\int\:_{-1}^{0}\frac{30e^{\frac{1}{x}}}{x^{3}}dx
area 11-x-2x^2, 8/(x^3)	area\:11-x-2x^{2},\frac{8}{x^{3}}
integral of 4/(x^2)	\int\:\frac{4}{x^{2}}dx
derivative of f(x)=2e^{3-4x}	derivative\:f(x)=2e^{3-4x}
integral from 0 to pi of 7sin^2(xco)s^4x	\int\:_{0}^{π}7\sin^{2}(xco)s^{4}xdx
sum from n=0 to infinity of (n^4)/(3^n)	\sum\:_{n=0}^{\infty\:}\frac{n^{4}}{3^{n}}
(\partial)/(\partial z)(rsin(t))	\frac{\partial\:}{\partial\:z}(r\sin(t))
derivative of arctan(cos(7x))	derivative\:\arctan(\cos(7x))
derivative of sqrt(x)+sqrt(y)+6	derivative\:\sqrt{x}+\sqrt{y}+6
integral from 0 to 8 of e^{-0.25t}	\int\:_{0}^{8}e^{-0.25t}dt
integral of sin(3x)sin(6x)	\int\:\sin(3x)\sin(6x)dx
derivative of [x^2(x^2+8x)]^6	derivative\:[x^{2}(x^{2}+8x)]^{6}
x^2(dy)/(dx)=y^2	x^{2}\frac{dy}{dx}=y^{2}
derivative of (x^4)/(16)+1/(2x^2)	derivative\:\frac{x^{4}}{16}+\frac{1}{2x^{2}}
integral of 1/(sqrt(16-4x^2))	\int\:\frac{1}{\sqrt{16-4x^{2}}}dx
integral of 1/(2y+1)	\int\:\frac{1}{2y+1}dy
limit as x approaches infinity of (-3)/x	\lim\:_{x\to\:\infty\:}(\frac{-3}{x})
inverse oflaplace 1/(s(s^2+1))	inverselaplace\:\frac{1}{s(s^{2}+1)}
limit as x approaches-2 of 4x^2	\lim\:_{x\to\:-2}(4x^{2})
integral of (0.7y^3+10+2y^{-3})	\int\:(0.7y^{3}+10+2y^{-3})dy
derivative of f(x)=x^2-2x-3	derivative\:f(x)=x^{2}-2x-3
derivative of sin(cot(x))	\frac{d}{dx}(\sin(\cot(x)))
tangent of y=e^xcos(x)	tangent\:y=e^{x}\cos(x)
inverse oflaplace (7s+5)/((s+2)(s-1))	inverselaplace\:\frac{7s+5}{(s+2)(s-1)}
integral from 0 to 1 of (x^3)	\int\:_{0}^{1}(x^{3})dx
taylor xcos(2x)	taylor\:x\cos(2x)
integral of ((ln^2(x^2)))/x	\int\:\frac{(\ln^{2}(x^{2}))}{x}dx
integral of (8x^3)/(sqrt(0.2x^4+8000))	\int\:\frac{8x^{3}}{\sqrt{0.2x^{4}+8000}}dx
(\partial)/(\partial y)(x^y+y)	\frac{\partial\:}{\partial\:y}(x^{y}+y)
limit as x approaches 3 of 1/(x+3)	\lim\:_{x\to\:3}(\frac{1}{x+3})
derivative of f(x)=4x^{10}e^x	derivative\:f(x)=4x^{10}e^{x}
integral of (t-2t^4)/(sqrt(t))	\int\:\frac{t-2t^{4}}{\sqrt{t}}dt
(\partial)/(\partial x)((x)^2+(y)^4)	\frac{\partial\:}{\partial\:x}((x)^{2}+(y)^{4})
derivative of (x^3)/(e^{1/x)}	derivative\:\frac{x^{3}}{e^{\frac{1}{x}}}
(\partial)/(\partial z)((xy^2)/(z^3))	\frac{\partial\:}{\partial\:z}(\frac{xy^{2}}{z^{3}})
(\partial)/(\partial x)((y-5x)/(y^2+4x^2))	\frac{\partial\:}{\partial\:x}(\frac{y-5x}{y^{2}+4x^{2}})
(\partial)/(\partial x)(x^{0.5}y)	\frac{\partial\:}{\partial\:x}(x^{0.5}y)
y^{''}-y^'-6y=0,y(0)=1,y^'(0)=4	y^{\prime\:\prime\:}-y^{\prime\:}-6y=0,y(0)=1,y^{\prime\:}(0)=4
integral from 0 to 3 of e^x	\int\:_{0}^{3}e^{x}dx
tangent of f(x)=sqrt(x+16),\at x=1	tangent\:f(x)=\sqrt{x+16},\at\:x=1
(dy)/(dx)=(y)	\frac{dy}{dx}=(y)
y^{''}+2y=3,y(0)=-1,y(0)=2	y^{\prime\:\prime\:}+2y=3,y(0)=-1,y(0)=2
(\partial)/(\partial t)(xz^2t)	\frac{\partial\:}{\partial\:t}(xz^{2}t)
(dy}{dx}=\frac{2x)/y+2/y+1/(xy)	\frac{dy}{dx}=\frac{2x}{y}+\frac{2}{y}+\frac{1}{xy}
derivative of y=arcsin(8x+1)	derivative\:y=\arcsin(8x+1)
sum from n=1 to infinity of (-3^n)/(8^n)	\sum\:_{n=1}^{\infty\:}\frac{-3^{n}}{8^{n}}
derivative of e^{2x}-3x	derivative\:e^{2x}-3x
3e^xtan(y)dx+(2-e^x)sec^2(y)dy=0	3e^{x}\tan(y)dx+(2-e^{x})\sec^{2}(y)dy=0
tangent of y=4x^3-4x(-1)	tangent\:y=4x^{3}-4x(-1)
derivative of ln(arccsc(x))	derivative\:\ln(\arccsc(x))
(\partial)/(\partial y)(x^3y^5)	\frac{\partial\:}{\partial\:y}(x^{3}y^{5})
y^'=(x-2)/(y-4)	y^{\prime\:}=\frac{x-2}{y-4}
tangent of f(x)=sqrt(x^2+9),\at x=-4	tangent\:f(x)=\sqrt{x^{2}+9},\at\:x=-4
integral of xos(x)	\int\:xos(x)dx
sum from n=1 to infinity of (e^n)/n	\sum\:_{n=1}^{\infty\:}\frac{e^{n}}{n}
ty^'+2y=t^2-t+1,y(1)=0.5	ty^{\prime\:}+2y=t^{2}-t+1,y(1)=0.5
derivative of sin^2(14x)	derivative\:\sin^{2}(14x)
tangent of f(x)=2x^2-4,\at x=8	tangent\:f(x)=2x^{2}-4,\at\:x=8
(\partial)/(\partial x)(zarctan(x/y))	\frac{\partial\:}{\partial\:x}(z\arctan(\frac{x}{y}))
integral of 6(x+2)*ln(x+2)	\int\:6(x+2)\cdot\:\ln(x+2)dx
derivative of (3x+2^2)	\frac{d}{dx}((3x+2)^{2})
integral of 4/y	\int\:\frac{4}{y}dy
derivative of x^3+1	derivative\:x^{3}+1

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