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Popular Calculus Problems

integral from 0 to infinity of integral from 0 to infinity of e^{-x-y}	\int\:_{0}^{\infty\:}\int\:_{0}^{\infty\:}e^{-x-y}dxdy
area y=x^3-5x,y=11x	area\:y=x^{3}-5x,y=11x
limit as x approaches 8 of (8/x-1)/(x-8)	\lim\:_{x\to\:8}(\frac{\frac{8}{x}-1}{x-8})
derivative of e^{-sqrt(x)}	derivative\:e^{-\sqrt{x}}
limit as x approaches 8 of 1/(x-8)	\lim\:_{x\to\:8}(\frac{1}{x-8})
tangent of 6/(x+4)	tangent\:\frac{6}{x+4}
limit as x approaches-2-of ln(x+3)	\lim\:_{x\to\:-2-}(\ln(x+3))
tangent of 2/(sqrt(1/4+h))-4	tangent\:\frac{2}{\sqrt{\frac{1}{4}+h}}-4
integral of x/((x^2+2x+2))	\int\:\frac{x}{(x^{2}+2x+2)}dx
tangent of y=x^4e^{-x},(1, 1/e)	tangent\:y=x^{4}e^{-x},(1,\frac{1}{e})
integral of 1/((100-x^2)^2)	\int\:\frac{1}{(100-x^{2})^{2}}dx
slope of (-2.3)(6.2)	slope\:(-2.3)(6.2)
integral of (sqrt(6x))/(6+sqrt(x))	\int\:\frac{\sqrt{6x}}{6+\sqrt{x}}dx
derivative of (1+2x/(sqrt(1-x^2)))	\frac{d}{dx}(\frac{1+2x}{\sqrt{1-x^{2}}})
(\partial)/(\partial x)((2z)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{2z}{x+y})
derivative of (2x+4x^2/((1+4x)^2))	\frac{d}{dx}(\frac{2x+4x^{2}}{(1+4x)^{2}})
limit as x approaches-5-of x/(x+5)	\lim\:_{x\to\:-5-}(\frac{x}{x+5})
slope ofintercept (50,43),(60,86)	slopeintercept\:(50,43),(60,86)
(dy)/(dx)=-10xy^2	\frac{dy}{dx}=-10xy^{2}
integral from 0 to infinity of e^{-8x}	\int\:_{0}^{\infty\:}e^{-8x}dx
y^{''}-6y^'+9y=t^{-5}e^{3t}	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=t^{-5}e^{3t}
derivative of ln(sin(x+y))	\frac{d}{dx}(\ln(\sin(x+y)))
derivative of f(x)=3x+6	derivative\:f(x)=3x+6
d/(dA)((1+cot(A))/(csc(A)))	\frac{d}{dA}(\frac{1+\cot(A)}{\csc(A)})
tangent of f(x)=x^4-3x^2+5,\at x=-1	tangent\:f(x)=x^{4}-3x^{2}+5,\at\:x=-1
(dy)/(dx)-y=x^2sin(x)	\frac{dy}{dx}-y=x^{2}\sin(x)
d/(dt)(t-sin(t))	\frac{d}{dt}(t-\sin(t))
(\partial)/(\partial y)(sin(x+y)+(x+y))	\frac{\partial\:}{\partial\:y}(\sin(x+y)+(x+y))
x^2y(dy)/(dx)=e^x	x^{2}y\frac{dy}{dx}=e^{x}
sum from n=1 to infinity of 3/(sqrt(n))	\sum\:_{n=1}^{\infty\:}\frac{3}{\sqrt{n}}
integral of 9sqrt(4-x^2)	\int\:9\sqrt{4-x^{2}}dx
(1/(xln(x)))^'	(\frac{1}{x\ln(x)})^{\prime\:}
derivative of (2x^2+6x+4)/(sqrt(x))	derivative\:\frac{2x^{2}+6x+4}{\sqrt{x}}
derivative of (ln(3x)/(7x^2))	\frac{d}{dx}(\frac{\ln(3x)}{7x^{2}})
tangent of f(x)= 1/x	tangent\:f(x)=\frac{1}{x}
limit as x approaches-8 of (x-8)/(\|x+8\|)	\lim\:_{x\to\:-8}(\frac{x-8}{\left\|x+8\right\|})
integral of 1/(x(ln(x))^pi)	\int\:\frac{1}{x(\ln(x))^{π}}dx
sum from n=0 to infinity of (-1)^n2^n	\sum\:_{n=0}^{\infty\:}(-1)^{n}2^{n}
integral of 1/(t^2sqrt(121-t^2))	\int\:\frac{1}{t^{2}\sqrt{121-t^{2}}}dt
integral of e^{2x}*x^2	\int\:e^{2x}\cdot\:x^{2}dx
(\partial)/(\partial x)(4(y^2-x^2)ln(x+y))	\frac{\partial\:}{\partial\:x}(4(y^{2}-x^{2})\ln(x+y))
integral of x^2*sqrt(1-x)	\int\:x^{2}\cdot\:\sqrt{1-x}dx
derivative of 1/(2x)-8/(5x^4)	derivative\:\frac{1}{2x}-\frac{8}{5x^{4}}
integral of (log_{e}(x))/x	\int\:\frac{\log_{e}(x)}{x}dx
derivative of f(x)=ln(10x)	derivative\:f(x)=\ln(10x)
taylor e^{5x+5}	taylor\:e^{5x+5}
limit as x approaches-infinity of x^2-x	\lim\:_{x\to\:-\infty\:}(x^{2}-x)
derivative of y=(3x^5+9)/(x^3)	derivative\:y=\frac{3x^{5}+9}{x^{3}}
inverse oflaplace (s^2-1)/((s-2)^6)	inverselaplace\:\frac{s^{2}-1}{(s-2)^{6}}
(dy)/(dx)+20y=sin(x)	\frac{dy}{dx}+20y=\sin(x)
derivative of 3arctan(x)	\frac{d}{dx}(3\arctan(x))
(d^3)/(dx^3)((x^2-1)^3)	\frac{d^{3}}{dx^{3}}((x^{2}-1)^{3})
integral from 0 to pi/2 of 15cos^5(x)	\int\:_{0}^{\frac{π}{2}}15\cos^{5}(x)dx
limit as x approaches-2+of-1/(x^2-4)	\lim\:_{x\to\:-2+}(-\frac{1}{x^{2}-4})
derivative of-ax+d/(x^2)	\frac{d}{dx}(-ax+\frac{d}{x^{2}})
inverse oflaplace s/((s^2+1)(s^2-2s+2))	inverselaplace\:\frac{s}{(s^{2}+1)(s^{2}-2s+2)}
integral of (x-5)/(x^2+9)	\int\:\frac{x-5}{x^{2}+9}dx
integral of x^2sin(2Ax)	\int\:x^{2}\sin(2Ax)dx
(dy)/(dx)=sqrt(4y)e^{x+10}	\frac{dy}{dx}=\sqrt{4y}e^{x+10}
derivative of (2x+2x^{1/2}/(6+x^{3/2)})	\frac{d}{dx}(\frac{2x+2x^{\frac{1}{2}}}{6+x^{\frac{3}{2}}})
integral of x^3cos(5x)	\int\:x^{3}\cos(5x)dx
integral of 20x^9	\int\:20x^{9}dx
tangent of f(x)=4sqrt(x)-1,\at x=16	tangent\:f(x)=4\sqrt{x}-1,\at\:x=16
area y=3x,y=x^2-4	area\:y=3x,y=x^{2}-4
y^'=x+6y	y^{\prime\:}=x+6y
derivative of ln(x/3+(x-3)/x)	\frac{d}{dx}(\ln(\frac{x}{3})+\frac{x-3}{x})
inverse oflaplace 3/(s(s-1)^3)	inverselaplace\:\frac{3}{s(s-1)^{3}}
f(x)=log_{10}(sqrt(1-x))	f(x)=\log_{10}(\sqrt{1-x})
integral of 30x	\int\:30xdx
derivative of a-b(x-c^{1/3})	\frac{d}{dx}(a-b(x-c)^{\frac{1}{3}})
integral of (x+1)e^{3x}	\int\:(x+1)e^{3x}dx
derivative of 1/2 tan^2(x)	\frac{d}{dx}(\frac{1}{2}\tan^{2}(x))
integral of sqrt(e^x-3)	\int\:\sqrt{e^{x}-3}dx
integral from-1 to 5 of (8x)/(x^2-4x-12)	\int\:_{-1}^{5}\frac{8x}{x^{2}-4x-12}dx
(\partial)/(\partial z)(x/y-y/z)	\frac{\partial\:}{\partial\:z}(\frac{x}{y}-\frac{y}{z})
integral of 1/((x-4)^{3/2)}	\int\:\frac{1}{(x-4)^{\frac{3}{2}}}dx
limit as x approaches 0 of x^{-5/(ln(x))}	\lim\:_{x\to\:0}(x^{-\frac{5}{\ln(x)}})
(\partial)/(\partial x)(x^2+3y^2)	\frac{\partial\:}{\partial\:x}(x^{2}+3y^{2})
tangent of f(x)=x^2+8,(5,33)	tangent\:f(x)=x^{2}+8,(5,33)
tangent of y= 8/x ,(2,4)	tangent\:y=\frac{8}{x},(2,4)
limit as x approaches infinity of x^3+x	\lim\:_{x\to\:\infty\:}(x^{3}+x)
integral of (4x+13)/(x^2+3x-10)	\int\:\frac{4x+13}{x^{2}+3x-10}dx
(\partial)/(\partial x)(2x^2y+2x)	\frac{\partial\:}{\partial\:x}(2x^{2}y+2x)
integral from 0 to 1 of xe^{-2x^2}	\int\:_{0}^{1}xe^{-2x^{2}}dx
slope of (-29)(-2-5)	slope\:(-29)(-2-5)
limit as x approaches-infinity of 3x^6	\lim\:_{x\to\:-\infty\:}(3x^{6})
inverse oflaplace (4s+20)/(s^2+8s+16)	inverselaplace\:\frac{4s+20}{s^{2}+8s+16}
(d^2)/(dx^2)(8/(9t^6))	\frac{d^{2}}{dx^{2}}(\frac{8}{9t^{6}})
(\partial)/(\partial y)(x^4)	\frac{\partial\:}{\partial\:y}(x^{4})
integral of 4	\int\:4dx
derivative of f(x)=(5x+1)^2	derivative\:f(x)=(5x+1)^{2}
area 32-8x,[2,4]	area\:32-8x,[2,4]
derivative of y=12sqrt(x)	derivative\:y=12\sqrt{x}
y^'=10xy-2x	y^{\prime\:}=10xy-2x
integral from-infinity to 0 of 1/(2-3x)	\int\:_{-\infty\:}^{0}\frac{1}{2-3x}dx
derivative of 1/((x-1^2+1))	\frac{d}{dx}(\frac{1}{(x-1)^{2}+1})
x^2 derivative of (dy/(dx))+19x(dy)/(dx)+145y=0	x^{2}\frac{d}{dx}(\frac{dy}{dx})+19x\frac{dy}{dx}+145y=0
5y^{''}+11y^'+7y=0,y(0)=8,y^'(0)=10	5y^{\prime\:\prime\:}+11y^{\prime\:}+7y=0,y(0)=8,y^{\prime\:}(0)=10
integral from 0 to 1 of 4x^3sqrt(3x^4+4)	\int\:_{0}^{1}4x^{3}\sqrt{3x^{4}+4}dx
integral of xsqrt((1-x^2))	\int\:x\sqrt{(1-x^{2})}dx

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