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Popular Calculus Problems

derivative of f(x)=-x^{4/3}	derivative\:f(x)=-x^{\frac{4}{3}}
integral from-1 to 1 of (8-8x^2)^2	\int\:_{-1}^{1}(8-8x^{2})^{2}dx
(\partial)/(\partial x)(y^2cos(xy))	\frac{\partial\:}{\partial\:x}(y^{2}\cos(xy))
integral of acos(x)	\int\:a\cos(x)dx
integral from 1 to 4 of 1/(4-sqrt(x))	\int\:_{1}^{4}\frac{1}{4-\sqrt{x}}dx
integral of 4x(x^2+28000)^{-2/3}	\int\:4x(x^{2}+28000)^{-\frac{2}{3}}dx
tangent of f(x)=5x^2-4x-2,\at x=(1-1)	tangent\:f(x)=5x^{2}-4x-2,\at\:x=(1-1)
integral from-3 to 0 of x/(sqrt(9-x^2))	\int\:_{-3}^{0}\frac{x}{\sqrt{9-x^{2}}}dx
area y=sqrt(x),y= 1/3 x,x=25	area\:y=\sqrt{x},y=\frac{1}{3}x,x=25
integral of (sqrt(x^2+16))/(2x)	\int\:\frac{\sqrt{x^{2}+16}}{2x}dx
integral from 0 to 8 of 1/((10-2x)^{1/5)}	\int\:_{0}^{8}\frac{1}{(10-2x)^{\frac{1}{5}}}dx
integral from 0 to infinity of e^{-x}	\int\:_{0}^{\infty\:}e^{-x}dx
integral of 1/(1-e^x)	\int\:\frac{1}{1-e^{x}}dx
limit as n approaches infinity of ln(n)	\lim\:_{n\to\:\infty\:}(\ln(n))
integral of (36)/(x^3-6x^2)	\int\:\frac{36}{x^{3}-6x^{2}}dx
integral of e^{9x+7}	\int\:e^{9x+7}dx
derivative of e^{3x+9}	\frac{d}{dx}(e^{3x+9})
tangent of (x^3-9x)^{10}(3)	tangent\:(x^{3}-9x)^{10}(3)
((2x)/(x^2+1))^'	(\frac{2x}{x^{2}+1})^{\prime\:}
limit as x approaches 4 of 4x^2-5x+1	\lim\:_{x\to\:4}(4x^{2}-5x+1)
derivative of ln(x+3)	derivative\:\ln(x+3)
derivative of sqrt(2x^2+7)	derivative\:\sqrt{2x^{2}+7}
y^'-2y=-1,y(0)=3	y^{\prime\:}-2y=-1,y(0)=3
(y-x)e^x+(1+e^x)y^'=0	(y-x)e^{x}+(1+e^{x})y^{\prime\:}=0
derivative of 10+(50t)/(2t^2+9)	derivative\:10+\frac{50t}{2t^{2}+9}
limit as x approaches-2 of 1/2	\lim\:_{x\to\:-2}(\frac{1}{2})
inverse oflaplace (-3e^{6-3s})/((s-2)(s-3)(s+2))	inverselaplace\:\frac{-3e^{6-3s}}{(s-2)(s-3)(s+2)}
limit as h approaches 0 of (x+h)^3-x^3	\lim\:_{h\to\:0}((x+h)^{3}-x^{3})
(\partial)/(\partial t)(2e^{sin(x+2ct)})	\frac{\partial\:}{\partial\:t}(2e^{\sin(x+2ct)})
(dx)/(dt)=-2x	\frac{dx}{dt}=-2x
integral of cos^2(2t)	\int\:\cos^{2}(2t)dt
y^{''}+9=0	y^{\prime\:\prime\:}+9=0
derivative of-2pisin(4pix)	derivative\:-2π\sin(4πx)
derivative of 230-8x+0.04x^2	\frac{d}{dx}(230-8x+0.04x^{2})
derivative of (csc(x*tan(x))/(cos(x)))	\frac{d}{dx}(\frac{\csc(x)\cdot\:\tan(x)}{\cos(x)})
(\partial)/(\partial x)((1-x^2-y^2)^{1/2})	\frac{\partial\:}{\partial\:x}((1-x^{2}-y^{2})^{\frac{1}{2}})
limit as x approaches pi/2+of 9/x sec(x)	\lim\:_{x\to\:\frac{π}{2}+}(\frac{9}{x}\sec(x))
(\partial)/(\partial y)(e^zcos(y))	\frac{\partial\:}{\partial\:y}(e^{z}\cos(y))
tangent of f(x)=(10)/(1+e^{-x)},\at x=0	tangent\:f(x)=\frac{10}{1+e^{-x}},\at\:x=0
sum from n=2 to infinity of ((n+1)/n)^n	\sum\:_{n=2}^{\infty\:}(\frac{n+1}{n})^{n}
integral of (5^x)/(1+5^x)	\int\:\frac{5^{x}}{1+5^{x}}dx
derivative of (1000+x^{-1/3})	\frac{d}{dx}((1000+x)^{-\frac{1}{3}})
integral of csc^2(x)cot^2(x)	\int\:\csc^{2}(x)\cot^{2}(x)dx
integral of 6x^2tan(x^3)	\int\:6x^{2}\tan(x^{3})dx
implicit (dy)/(dx),16x^2-16xy+y^2=1	implicit\:\frac{dy}{dx},16x^{2}-16xy+y^{2}=1
tangent of f(x)=(x^3-9x)^8,(-3,0)	tangent\:f(x)=(x^{3}-9x)^{8},(-3,0)
(dy)/(dx)+3y=2x	\frac{dy}{dx}+3y=2x
area x^3,x,0,1	area\:x^{3},x,0,1
limit as x approaches 4 of 9/(9-(-3))	\lim\:_{x\to\:4}(\frac{9}{9-(-3)})
limit as x approaches 0 of x^2*ln(x)	\lim\:_{x\to\:0}(x^{2}\cdot\:\ln(x))
derivative of (x-pi^2)	\frac{d}{dx}((x-π)^{2})
integral from 1 to 2 of 1/(x^2)	\int\:_{1}^{2}\frac{1}{x^{2}}dx
derivative of 4*sin(x)	\frac{d}{dx}(4\cdot\:\sin(x))
maclaurin sin(x^2), pi/4	maclaurin\:\sin(x^{2}),\frac{π}{4}
sum from n=1 to infinity of n*(4/5)^n	\sum\:_{n=1}^{\infty\:}n\cdot\:(\frac{4}{5})^{n}
limit as x approaches 0+of x(ln(x))	\lim\:_{x\to\:0+}(x(\ln(x)))
tangent of 4x^2-3x+2	tangent\:4x^{2}-3x+2
integral from 1 to 3 of x^4	\int\:_{1}^{3}x^{4}dx
f^'(x)=2x+3x^{1.7}	f^{\prime\:}(x)=2x+3x^{1.7}
derivative of 1/(x(ln(x)^{2/3)})	\frac{d}{dx}(\frac{1}{x(\ln(x))^{\frac{2}{3}}})
d/(dθ)((sin(θ))/(1+cos(θ)))	\frac{d}{dθ}(\frac{\sin(θ)}{1+\cos(θ)})
(\partial)/(\partial z)(2xz^2cos(y))	\frac{\partial\:}{\partial\:z}(2xz^{2}\cos(y))
limit as x approaches 0 of (x^2)/(x+1)	\lim\:_{x\to\:0}(\frac{x^{2}}{x+1})
integral of sin^3(x)cos^{16}(x)	\int\:\sin^{3}(x)\cos^{16}(x)dx
limit as y approaches 0 of (x^y-1)/y	\lim\:_{y\to\:0}(\frac{x^{y}-1}{y})
derivative of 8sqrt(8x^2+5)	derivative\:8\sqrt{8x^{2}+5}
limit as x approaches 0-of 4/(sin(x))	\lim\:_{x\to\:0-}(\frac{4}{\sin(x)})
integral of xe^{-ax^2}	\int\:xe^{-ax^{2}}dx
y^'=4e^{x+y}	y^{\prime\:}=4e^{x+y}
derivative of 4x^2-5x	derivative\:4x^{2}-5x
(\partial)/(\partial x)(sin(xe^{x^2y}))	\frac{\partial\:}{\partial\:x}(\sin(x\cdot\:e^{x^{2}\cdot\:y}))
integral of (sin^3(2t))sqrt(cos(2t))	\int\:(\sin^{3}(2t))\sqrt{\cos(2t)}dt
limit as x approaches 9+of ln(x^2-81)	\lim\:_{x\to\:9+}(\ln(x^{2}-81))
integral of e^xsqrt(6-e^x)	\int\:e^{x}\sqrt{6-e^{x}}dx
(3x^2)^'	(3x^{2})^{\prime\:}
integral of (x^2)/(sqrt(x^6+1))	\int\:\frac{x^{2}}{\sqrt{x^{6}+1}}dx
integral of (20)/(x+5)	\int\:\frac{20}{x+5}dx
slope ofintercept (2,1),(8,7)	slopeintercept\:(2,1),(8,7)
derivative of (f(x))^{g(x)}	derivative\:(f(x))^{g(x)}
taylor e^{-x/2}0	taylor\:e^{-\frac{x}{2}}0
derivative of f(x)=ln(x+sqrt(x^2+1))	derivative\:f(x)=\ln(x+\sqrt{x^{2}+1})
derivative of x^2sin(x+2)	\frac{d}{dx}(x^{2}\sin(x)+2)
integral of 1/(\sqrt[5]{e^{2t)}}	\int\:\frac{1}{\sqrt[5]{e^{2t}}}dt
integral of (7+e)	\int\:(7+e)dx
integral from 1 to infinity of (ln(x))/x	\int\:_{1}^{\infty\:}\frac{\ln(x)}{x}dx
derivative of x^4-1/x	\frac{d}{dx}(x^{4}-\frac{1}{x})
limit as x approaches 4 of x^2-4x+1	\lim\:_{x\to\:4}(x^{2}-4x+1)
derivative of f(x)=sqrt(3x-5)	derivative\:f(x)=\sqrt{3x-5}
integral of (16x^2)/((x-9)(x+3)^2)	\int\:\frac{16x^{2}}{(x-9)(x+3)^{2}}dx
derivative of (5x-4(2x^3-x^2+1))	\frac{d}{dx}((5x-4)(2x^{3}-x^{2}+1))
tangent of f(x)= 1/(4+3x),(1, 1/7)	tangent\:f(x)=\frac{1}{4+3x},(1,\frac{1}{7})
derivative of e^{9sqrt(x)}	derivative\:e^{9\sqrt{x}}
derivative of f(x)=2x^2-4x+1	derivative\:f(x)=2x^{2}-4x+1
integral of 1/(x^{5/8)-x^{1/8}}	\int\:\frac{1}{x^{\frac{5}{8}}-x^{\frac{1}{8}}}dx
integral of 31arctan(sqrt(x))	\int\:31\arctan(\sqrt{x})dx
integral from 1 to 4 of 3x^{1/3}	\int\:_{1}^{4}3x^{\frac{1}{3}}dx
derivative of log_{2}(7x^2+x-2)	\frac{d}{dx}(\log_{2}(7x^{2}+x-2))
derivative of 12x-x^2	\frac{d}{dx}(12x-x^{2})
limit as x approaches 1 of ((x+1))/(x-1)	\lim\:_{x\to\:1}(\frac{(x+1)}{x-1})
derivative of x^2-1/8 ln(x)	\frac{d}{dx}(x^{2}-\frac{1}{8}\ln(x))

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