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Popular Calculus Problems

derivative of 1/3 x^3+x^2-x+5	\frac{d}{dx}(\frac{1}{3}x^{3}+x^{2}-x+5)
limit as n approaches infinity of sin((npi)/2)	\lim\:_{n\to\:\infty\:}(\sin(\frac{nπ}{2}))
integral of (e^{2x})/(sqrt(1-e^{2x))}	\int\:\frac{e^{2x}}{\sqrt{1-e^{2x}}}dx
limit as x approaches 3-of (x^2-9)/(x-3)	\lim\:_{x\to\:3-}(\frac{x^{2}-9}{x-3})
(\partial)/(\partial y)(cos(nx)e^{ny})	\frac{\partial\:}{\partial\:y}(\cos(nx)e^{ny})
integral of 9/(x^2sqrt(x^2+36))	\int\:\frac{9}{x^{2}\sqrt{x^{2}+36}}dx
integral of sin(4x)sin(2x)	\int\:\sin(4x)\sin(2x)dx
limit as x approaches-1 of x/(x^2-1)	\lim\:_{x\to\:-1}(\frac{x}{x^{2}-1})
derivative of (x^3+3x)/(x^2-4x+3)	derivative\:\frac{x^{3}+3x}{x^{2}-4x+3}
limit as x approaches 4-of (\|x-4\|)/(x-4)	\lim\:_{x\to\:4-}(\frac{\left\|x-4\right\|}{x-4})
integral of (x^3+x)sqrt(x^4+2x^2)	\int\:(x^{3}+x)\sqrt{x^{4}+2x^{2}}dx
(\partial)/(\partial x)(sin(xz^2)-xy^2)	\frac{\partial\:}{\partial\:x}(\sin(xz^{2})-xy^{2})
integral of xae^{-ax}	\int\:xae^{-ax}dx
y^'+3ty=t,y(0)=1	y^{\prime\:}+3ty=t,y(0)=1
integral of 9/(x(ln(x))^2)	\int\:\frac{9}{x(\ln(x))^{2}}dx
limit as x approaches 0 of x(cot(2x))	\lim\:_{x\to\:0}(x(\cot(2x)))
area sqrt(x),x^2	area\:\sqrt{x},x^{2}
derivative of 1+x^3	\frac{d}{dx}(1+x^{3})
tangent of f(x)=sqrt(5x+6),\at x=2	tangent\:f(x)=\sqrt{5x+6},\at\:x=2
x(dy)/(dx)+2y=8x^2	x\frac{dy}{dx}+2y=8x^{2}
sum from n=0 to infinity of 5/(4^n)	\sum\:_{n=0}^{\infty\:}\frac{5}{4^{n}}
integral of ln(6x+7)	\int\:\ln(6x+7)dx
(1+cos(t))y^'=(1-e^{-y})sin(t)	(1+\cos(t))y^{\prime\:}=(1-e^{-y})\sin(t)
integral of x^2(x^3-4)^3	\int\:x^{2}(x^{3}-4)^{3}dx
derivative of (6x/(x^2+3))	\frac{d}{dx}(\frac{6x}{x^{2}+3})
derivative of (x-7/((x+5)^{10)})	\frac{d}{dx}(\frac{x-7}{(x+5)^{10}})
derivative of x^2-12x+k	derivative\:x^{2}-12x+k
limit as x approaches 4 of xsqrt(25-x^2)	\lim\:_{x\to\:4}(x\sqrt{25-x^{2}})
y^{''}+4y^'+12y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+12y=0
integral from 0 to 4 of (13-t)sqrt(t)	\int\:_{0}^{4}(13-t)\sqrt{t}dt
derivative of y=t^2+5cos(t)	derivative\:y=t^{2}+5\cos(t)
(dy)/(dx)sin(x+y)=0	\frac{dy}{dx}\sin(x+y)=0
integral of (sec(x)+cos(x))/(4cos(x))	\int\:\frac{\sec(x)+\cos(x)}{4\cos(x)}dx
limit as x approaches 0 of x*log_{2}(x)	\lim\:_{x\to\:0}(x\cdot\:\log_{2}(x))
integral of (sqrt(x^2+36))/x	\int\:\frac{\sqrt{x^{2}+36}}{x}dx
limit as t approaches 3 of 4t^2-2t+1	\lim\:_{t\to\:3}(4t^{2}-2t+1)
derivative of f(x)=\sqrt[5]{5+2x+x^3}	\frac{d}{dx}f(x)=\sqrt[5]{5+2x+x^{3}}
(\partial)/(\partial x)(sin(pixy))	\frac{\partial\:}{\partial\:x}(\sin(πxy))
area 2x-1, 1/x ,x=3	area\:2x-1,\frac{1}{x},x=3
(dy)/(dx)= 1/((2x+y+1))	\frac{dy}{dx}=\frac{1}{(2x+y+1)}
(dy)/(dt)= y/t	\frac{dy}{dt}=\frac{y}{t}
area y=(x^2-4x-4)/(x^2-4x-5),y=0	area\:y=\frac{x^{2}-4x-4}{x^{2}-4x-5},y=0
6t((dy)/(dt))+y=t^3	6t(\frac{dy}{dt})+y=t^{3}
derivative of 4x^3+x+5sin(x)	\frac{d}{dx}(4x^{3}+x+5\sin(x))
integral of 2+3x^2-8x^3	\int\:2+3x^{2}-8x^{3}dx
tangent of f(x)=-4-3x^2,(2,-16)	tangent\:f(x)=-4-3x^{2},(2,-16)
integral from-45 to 0 of 1/(sqrt(4-x))	\int\:_{-45}^{0}\frac{1}{\sqrt{4-x}}dx
sum from n=1 to infinity of 8^{-n}	\sum\:_{n=1}^{\infty\:}8^{-n}
(\partial)/(\partial x)(1+e^{-xy}cos(y))	\frac{\partial\:}{\partial\:x}(1+e^{-xy}\cos(y))
integral of 2cos(4x)cos(2x)	\int\:2\cos(4x)\cos(2x)dx
integral of 4sqrt(1-x^2)	\int\:4\sqrt{1-x^{2}}dx
derivative of (5x-2x^4)^3	derivative\:(5x-2x^{4})^{3}
(x^{-2})^'	(x^{-2})^{\prime\:}
integral from 2 to 3 of 1/x	\int\:_{2}^{3}\frac{1}{x}dx
integral of (6x^2-3x+3)	\int\:(6x^{2}-3x+3)dx
derivative of cos(2-3x)	\frac{d}{dx}(\cos(2-3x))
(dy)/(dt)+e^ty=e^t	\frac{dy}{dt}+e^{t}y=e^{t}
(d^2y)/(dx^2)-4(dy)/(dx)+2y=0	\frac{d^{2}y}{dx^{2}}-4\frac{dy}{dx}+2y=0
limit as x approaches-(7pi)/2-of sec(x)	\lim\:_{x\to\:-\frac{7π}{2}-}(\sec(x))
(dy)/(dx)=9-y/(6x+250)	\frac{dy}{dx}=9-\frac{y}{6x+250}
tangent of f(x)=x^4+2x^2-x,\at x=1	tangent\:f(x)=x^{4}+2x^{2}-x,\at\:x=1
x^2y^'+xy=5	x^{2}y^{\prime\:}+xy=5
derivative of 9x^4+6x^3+1	\frac{d}{dx}(9x^{4}+6x^{3}+1)
integral of ln(sqrt(x)+sqrt(1+x))	\int\:\ln(\sqrt{x}+\sqrt{1+x})dx
derivative of log_{10}(x^7+5)	derivative\:\log_{10}(x^{7}+5)
derivative of 1/(3x^{2/3})	\frac{d}{dx}(\frac{1}{3x^{\frac{2}{3}}})
integral of sqrt(x)(x^2-1/x)	\int\:\sqrt{x}(x^{2}-\frac{1}{x})dx
(\partial)/(\partial x)(e^x+cos(y))	\frac{\partial\:}{\partial\:x}(e^{x}+\cos(y))
derivative of f(x)=(3x-7)/(5x-2)	derivative\:f(x)=\frac{3x-7}{5x-2}
derivative of 2/3 x^2-5x+3/x+7	\frac{d}{dx}(\frac{2}{3}x^{2}-5x+\frac{3}{x}+7)
area y=20-x,y=sqrt(x),y=1	area\:y=20-x,y=\sqrt{x},y=1
y^'=-ay(1+3y)	y^{\prime\:}=-ay(1+3y)
(\partial)/(\partial y)(100e^{-2x^2-y^2})	\frac{\partial\:}{\partial\:y}(100e^{-2x^{2}-y^{2}})
integral of (5sin^3(x))/(cos(x))	\int\:\frac{5\sin^{3}(x)}{\cos(x)}dx
(\partial)/(\partial x)(x^3y)	\frac{\partial\:}{\partial\:x}(x^{3}y)
integral of (x^8+1)e^{x^9+9x}	\int\:(x^{8}+1)e^{x^{9}+9x}dx
y^{''}+19y=0	y^{\prime\:\prime\:}+19y=0
limit as x approaches-5-of (\|5-x\|)/(5-x)	\lim\:_{x\to\:-5-}(\frac{\left\|5-x\right\|}{5-x})
integral of (x^2+36x-9)/(x^3-9x)	\int\:\frac{x^{2}+36x-9}{x^{3}-9x}dx
integral from 0 to pi/2 of tan^2(x)	\int\:_{0}^{\frac{π}{2}}\tan^{2}(x)dx
(\partial)/(\partial y)(1+x^2)	\frac{\partial\:}{\partial\:y}(1+x^{2})
derivative of arctan(x/4)	derivative\:\arctan(\frac{x}{4})
integral of ((4-x)^2)/(sqrt(x))	\int\:\frac{(4-x)^{2}}{\sqrt{x}}dx
derivative of (e^x)/(e^x+3)	derivative\:\frac{e^{x}}{e^{x}+3}
(dy)/(dx)=2xe^{-y}	\frac{dy}{dx}=2xe^{-y}
integral of (4x)/(sqrt(x^2+1))	\int\:\frac{4x}{\sqrt{x^{2}+1}}dx
integral of x^2*2^x	\int\:x^{2}\cdot\:2^{x}dx
derivative of f(x)=sqrt(x)+x^{2/3}-3x	derivative\:f(x)=\sqrt{x}+x^{\frac{2}{3}}-3x
limit as x approaches 0 of 2sin(x)ln(x)	\lim\:_{x\to\:0}(2\sin(x)\ln(x))
derivative of 2e^x-e^{x+1}+e^{2/3}-5pi^2	derivative\:2e^{x}-e^{x+1}+e^{\frac{2}{3}}-5π^{2}
limit as x approaches 0+of sin^2(x)	\lim\:_{x\to\:0+}(\sin^{2}(x))
sum from n=0 to infinity of (3/2)^n	\sum\:_{n=0}^{\infty\:}(\frac{3}{2})^{n}
derivative of (4x+asqrt(1+x)/(x^2-1))	\frac{d}{dx}(\frac{4x+a\sqrt{1+x}}{x^{2}-1})
dx+e^{2x}dy=0	dx+e^{2x}dy=0
derivative of A/(y^{14)}+Be^y	derivative\:\frac{A}{y^{14}}+Be^{y}
limit as x approaches 2-of-3	\lim\:_{x\to\:2-}(-3)
derivative of xsin(tan(x))	\frac{d}{dx}(x\sin(\tan(x)))
tangent of y=3x^2+2x^2+1,(-1,0)	tangent\:y=3x^{2}+2x^{2}+1,(-1,0)
limit as x approaches 2 of x^2+2x+1	\lim\:_{x\to\:2}(x^{2}+2x+1)
limit as x approaches infinity of x+x+x	\lim\:_{x\to\:\infty\:}(x+x+x)

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