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Popular Calculus Problems

integral from 0 to 6 of pi/9 (36-y^2)	\int\:_{0}^{6}\frac{π}{9}(36-y^{2})dy
(sin(x)-xcos(x))^'	(\sin(x)-x\cos(x))^{\prime\:}
y^'=20sqrt(x)y	y^{\prime\:}=20\sqrt{x}y
integral of 3xsin(1/6 x)	\int\:3x\sin(\frac{1}{6}x)dx
derivative of f(x)=-1/x	derivative\:f(x)=-\frac{1}{x}
sum from n=1 to infinity of 6sin(1/n)	\sum\:_{n=1}^{\infty\:}6\sin(\frac{1}{n})
inverse oflaplace (12(s+1))/(s(s^2+9))	inverselaplace\:\frac{12(s+1)}{s(s^{2}+9)}
(\partial)/(\partial x)(cos(3y))	\frac{\partial\:}{\partial\:x}(\cos(3y))
derivative of x/(sqrt(x-6))	\frac{d}{dx}(\frac{x}{\sqrt{x-6}})
integral of 1/4 x^2	\int\:\frac{1}{4}x^{2}dx
integral of 2x(x^2+4)^2	\int\:2x(x^{2}+4)^{2}dx
laplacetransform t-(t-5)(-(t-5))	laplacetransform\:t-(t-5)(-(t-5))
tangent of f(x)=2x^2-7,\at x=-2	tangent\:f(x)=2x^{2}-7,\at\:x=-2
area 4x+y^2=13,x=3y	area\:4x+y^{2}=13,x=3y
(ln(3x))^'	(\ln(3x))^{\prime\:}
laplacetransform 6e^{-5t}+5t	laplacetransform\:6e^{-5t}+5t
(\partial)/(\partial x)((x^2+y)(x-y^2))	\frac{\partial\:}{\partial\:x}((x^{2}+y)(x-y^{2}))
integral of x^{31}sin(x^{32})	\int\:x^{31}\sin(x^{32})dx
xy^'+y=46sqrt(x)	xy^{\prime\:}+y=46\sqrt{x}
maclaurin e^{(-3x)}	maclaurin\:e^{(-3x)}
derivative of y=(3x^4+9)/(x^2)	derivative\:y=\frac{3x^{4}+9}{x^{2}}
derivative of (x^3-2x^2+4)/(x^2)	derivative\:\frac{x^{3}-2x^{2}+4}{x^{2}}
integral of (ln(x+1))^2	\int\:(\ln(x+1))^{2}dx
derivative of 2e^{2x}cos(x-e^{2x}sin(x))	\frac{d}{dx}(2e^{2x}\cos(x)-e^{2x}\sin(x))
derivative of e^{12x-x^6}	\frac{d}{dx}(e^{12x-x^{6}})
integral of cot^4(5x)	\int\:\cot^{4}(5x)dx
integral of cos(y^4)	\int\:\cos(y^{4})dy
limit as x approaches 3 of (x-3)/(2x+4)	\lim\:_{x\to\:3}(\frac{x-3}{2x+4})
derivative of f(x)=((x+8)/(x-8))^5	derivative\:f(x)=(\frac{x+8}{x-8})^{5}
integral of (-e^{1/x})/(x^2)	\int\:\frac{-e^{\frac{1}{x}}}{x^{2}}dx
integral of (x-y)	\int\:(x-y)dx
(\partial)/(\partial x)(e^{4e^x})	\frac{\partial\:}{\partial\:x}(e^{4e^{x}})
derivative of x+2/x	derivative\:x+\frac{2}{x}
derivative of 3^{sin(x}+(e^{-x})/2)	\frac{d}{dx}(3^{\sin(x)}+\frac{e^{-x}}{2})
derivative of 5(sin(x^2)+2x^2cos(x^2))	derivative\:5(\sin(x^{2})+2x^{2}\cos(x^{2}))
integral of \sqrt[8]{cot(x)}csc^2(x)	\int\:\sqrt[8]{\cot(x)}\csc^{2}(x)dx
derivative of sqrt(49-x^2-y^2)	\frac{d}{dx}(\sqrt{49-x^{2}-y^{2}})
derivative of sqrt(cx)	\frac{d}{dx}(\sqrt{cx})
integral of 2/(x^3+3x^2+2x)	\int\:\frac{2}{x^{3}+3x^{2}+2x}dx
integral of 1/(a^2u^2)	\int\:\frac{1}{a^{2}u^{2}}du
tangent of f(x)=x^2-4,(-3,5)	tangent\:f(x)=x^{2}-4,(-3,5)
(dy)/(dt)=1.5y,y(0)=100	\frac{dy}{dt}=1.5y,y(0)=100
integral from 0 to infinity of te^{-bt}	\int\:_{0}^{\infty\:}te^{-bt}dt
tangent of f(x)=-8x^4+11x^2-3,(1,0)	tangent\:f(x)=-8x^{4}+11x^{2}-3,(1,0)
integral of 2/(x^2+3x)	\int\:\frac{2}{x^{2}+3x}dx
integral of ((sin(x)))/(cos(x))	\int\:\frac{(\sin(x))}{\cos(x)}dx
integral of (x^{1/3}-x^{1/4})/(4x^{1/2)}	\int\:\frac{x^{\frac{1}{3}}-x^{\frac{1}{4}}}{4x^{\frac{1}{2}}}dx
integral of 1/(2+2cos(x))	\int\:\frac{1}{2+2\cos(x)}dx
(dy)/(dx)=xe^{x^2-y}	\frac{dy}{dx}=xe^{x^{2}-y}
integral of x^3*e^{x^2}	\int\:x^{3}\cdot\:e^{x^{2}}dx
integral of 8/(sqrt(x))+8sqrt(x)	\int\:\frac{8}{\sqrt{x}}+8\sqrt{x}dx
(\partial)/(\partial y)(x/((x^3+y^2)))	\frac{\partial\:}{\partial\:y}(\frac{x}{(x^{3}+y^{2})})
derivative of y=-(e^{-x})/2 cos(2x)	derivative\:y=-\frac{e^{-x}}{2}\cos(2x)
tangent of f(x)=x^3-4x^2-1	tangent\:f(x)=x^{3}-4x^{2}-1
(dy)/(dt)=-y/t-8	\frac{dy}{dt}=-\frac{y}{t}-8
derivative of e^{4x}cos(3x)	\frac{d}{dx}(e^{4x}\cos(3x))
integral of sin(4x)cos(4x)	\int\:\sin(4x)\cos(4x)dx
derivative of y=6e^x+2/(\sqrt[3]{x)}	derivative\:y=6e^{x}+\frac{2}{\sqrt[3]{x}}
integral of 3/(2x^2-4x+10)	\int\:\frac{3}{2x^{2}-4x+10}dx
derivative of x^3sqrt(5-x^2)	\frac{d}{dx}(x^{3}\sqrt{5-x^{2}})
implicit (dy)/(dx),x^2+y^2=25	implicit\:\frac{dy}{dx},x^{2}+y^{2}=25
limit as x approaches 2 of [g(x)]^3	\lim\:_{x\to\:2}([g(x)]^{3})
derivative of f(x)=(e^{2x})/(sin(3x))	derivative\:f(x)=\frac{e^{2x}}{\sin(3x)}
parity ,(x+3)^{11}	parity\:,(x+3)^{11}
tangent of 2x^2-3x,\at x=4	tangent\:2x^{2}-3x,\at\:x=4
(dx)/(dt)=4xt^5	\frac{dx}{dt}=4xt^{5}
area y=x^2-1,y=5-x	area\:y=x^{2}-1,y=5-x
derivative of f(x)=5x+4/x	derivative\:f(x)=5x+\frac{4}{x}
derivative of 5/(1-4x^2)	\frac{d}{dx}(\frac{5}{1-4x^{2}})
derivative of (x+2)/(x^3+x-6)	derivative\:\frac{x+2}{x^{3}+x-6}
derivative of x/(x^2+196)	\frac{d}{dx}(\frac{x}{x^{2}+196})
limit as x approaches 14 of sqrt(x+2)	\lim\:_{x\to\:14}(\sqrt{x+2})
derivative of g(x)=ln(xe^{-9x})	derivative\:g(x)=\ln(xe^{-9x})
area 4x+12,x^2	area\:4x+12,x^{2}
integral of sech(4x)tanh(4x)	\int\:\sech(4x)\tanh(4x)dx
area 5cos(7x),5-5cos(7x)	area\:5\cos(7x),5-5\cos(7x)
derivative of 6e^{2x}	\frac{d}{dx}(6e^{2x})
limit as x approaches 8 of f(x)	\lim\:_{x\to\:8}(f(x))
integral of 1/(x^2+x-2)	\int\:\frac{1}{x^{2}+x-2}dx
(\partial)/(\partial x)(7y-5x)	\frac{\partial\:}{\partial\:x}(7y-5x)
integral of sin(1-2x)	\int\:\sin(1-2x)dx
(dy)/(dx)=1+x+y^2+xy^2	\frac{dy}{dx}=1+x+y^{2}+xy^{2}
limit as x approaches 2+of 2/(x-2)	\lim\:_{x\to\:2+}(\frac{2}{x-2})
limit as x approaches 1 of 7x+5	\lim\:_{x\to\:1}(7x+5)
(dy)/(dx)=(y-1)(y+1),y(0)=3	\frac{dy}{dx}=(y-1)(y+1),y(0)=3
area e^{3x},e^{7x},x=1	area\:e^{3x},e^{7x},x=1
sum from n=1 to infinity of (1.06)^n	\sum\:_{n=1}^{\infty\:}(1.06)^{n}
limit as x approaches-2 of (2x^2)/(2x+2)	\lim\:_{x\to\:-2}(\frac{2x^{2}}{2x+2})
derivative of x-5+1/x	derivative\:x-5+\frac{1}{x}
derivative of x^{9x}	derivative\:x^{9x}
y^'+8(tan(8x))*y=-9cos(8x)	y^{\prime\:}+8(\tan(8x))\cdot\:y=-9\cos(8x)
slope ofintercept (0.5)(7.9)	slopeintercept\:(0.5)(7.9)
integral of 9e^{5x+e^{5x}}	\int\:9e^{5x+e^{5x}}dx
integral of x(4x-1)^4	\int\:x(4x-1)^{4}dx
integral of 1/(sqrt(4+(u+3)))	\int\:\frac{1}{\sqrt{4+(u+3)}}du
derivative of y=ln(8x)	derivative\:y=\ln(8x)
y^{''}-7y^'=5t	y^{\prime\:\prime\:}-7y^{\prime\:}=5t
limit as x approaches 0 of x/(sin(4x))	\lim\:_{x\to\:0}(\frac{x}{\sin(4x)})
integral from 2 to 4 of 1/(sqrt(x^2+1))	\int\:_{2}^{4}\frac{1}{\sqrt{x^{2}+1}}dx
(\partial)/(\partial x)(y^{7x})	\frac{\partial\:}{\partial\:x}(y^{7x})

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