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Popular Calculus Problems

tangent of y=(x^2+4)(x^3-4x),(-2,0)	tangent\:y=(x^{2}+4)(x^{3}-4x),(-2,0)
limit as x approaches-2 of x^2-3x+1	\lim\:_{x\to\:-2}(x^{2}-3x+1)
inverse oflaplace pi/((s^2+pi)^2)	inverselaplace\:\frac{π}{(s^{2}+π)^{2}}
integral of ((x^2+5))/(x^3-x^2+x+3)	\int\:\frac{(x^{2}+5)}{x^{3}-x^{2}+x+3}dx
integral of (e^{-sx})	\int\:(e^{-sx})dx
tangent of y=sin(sin(x)),(4pi,0)	tangent\:y=\sin(\sin(x)),(4π,0)
limit as x approaches 0 of x^{5sin(x)}	\lim\:_{x\to\:0}(x^{5\sin(x)})
limit as x approaches infinity of 3/5	\lim\:_{x\to\:\infty\:}(\frac{3}{5})
(dx}{dy}=\frac{x^2)/y	\frac{dx}{dy}=\frac{x^{2}}{y}
inverse oflaplace s/(s^2-2s+26)	inverselaplace\:\frac{s}{s^{2}-2s+26}
(\partial)/(\partial x)(sin(x)cos(x))	\frac{\partial\:}{\partial\:x}(\sin(x)\cos(x))
(\partial)/(\partial y)(xy^2z^3)	\frac{\partial\:}{\partial\:y}(xy^{2}z^{3})
area y=sqrt(x),y=\sqrt[3]{x}	area\:y=\sqrt{x},y=\sqrt[3]{x}
integral of 1/(1+tan(β))	\int\:\frac{1}{1+\tan(β)}dβ
limit as x approaches 8 of (x^2-sqrt(8x))/(x^3+2x^2)	\lim\:_{x\to\:8}(\frac{x^{2}-\sqrt{8x}}{x^{3}+2x^{2}})
derivative of x*ln(2)	\frac{d}{dx}(x\cdot\:\ln(2))
derivative of f(x)=2+3sqrt(x)	derivative\:f(x)=2+3\sqrt{x}
derivative of (5x^2+3)(2x-5)	derivative\:(5x^{2}+3)(2x-5)
tangent of 16sqrt(x)	tangent\:16\sqrt{x}
integral of 1/(sqrt(4x^2-25))	\int\:\frac{1}{\sqrt{4x^{2}-25}}dx
y^'=-(1+y)^4	y^{\prime\:}=-(1+y)^{4}
limit as x approaches 0 of 3x^4+17x^2+1	\lim\:_{x\to\:0}(3x^{4}+17x^{2}+1)
integral of t^4e^{-st}	\int\:t^{4}e^{-st}dt
derivative of (5xln(3x+1)/(1-e^{2x)})	\frac{d}{dx}(\frac{5x\ln(3x+1)}{1-e^{2x}})
integral of-4log_{7}(t)	\int\:-4\log_{7}(t)dt
integral from 0 to 1 of 7cos(3x)	\int\:_{0}^{1}7\cos(3x)dx
derivative of (a+xsqrt(a-x))	\frac{d}{dx}((a+x)\sqrt{a-x})
d/(dθ)(θ)	\frac{d}{dθ}(θ)
(\partial)/(\partial x)(sin(7x^2y-3xy^3))	\frac{\partial\:}{\partial\:x}(\sin(7x^{2}y-3xy^{3}))
maclaurin (e^x-e^{-x})/2	maclaurin\:\frac{e^{x}-e^{-x}}{2}
integral of ((sec^3(x)))/(tan(x))	\int\:\frac{(\sec^{3}(x))}{\tan(x)}dx
limit as x approaches 1000 of x^{7/3}	\lim\:_{x\to\:1000}(x^{\frac{7}{3}})
integral of ((5-50x))/(sqrt(36-25x^2))	\int\:\frac{(5-50x)}{\sqrt{36-25x^{2}}}dx
limit as x approaches infinity of (\frac{x+1)/((x+1)^2+1)}{x/(x^2+1)}	\lim\:_{x\to\:\infty\:}(\frac{\frac{x+1}{(x+1)^{2}+1}}{\frac{x}{x^{2}+1}})
derivative of (1-5x/(6+x))	\frac{d}{dx}(\frac{1-5x}{6+x})
derivative of cosh(xcos(x^2))	\frac{d}{dx}(\cosh(x)\cos(x^{2}))
derivative of sin(pi/(12))	\frac{d}{dx}(\sin(\frac{π}{12}))
derivative of arctan(8/x)	\frac{d}{dx}(\arctan(\frac{8}{x}))
derivative of sqrt(x+\sqrt{x+1)}	\frac{d}{dx}(\sqrt{x+\sqrt{x+1}})
area y=-x^2+16,y=(-x)/4-1,4(y+6.5)=6.5x	area\:y=-x^{2}+16,y=\frac{-x}{4}-1,4(y+6.5)=6.5x
derivative of (3x^2-6x+6)e^{-5x}	derivative\:(3x^{2}-6x+6)e^{-5x}
integral from 0 to 2 of sin^2(xco)s^22x	\int\:_{0}^{2}\sin^{2}(xco)s^{2}2x
integral of 5/(4+9x^2)	\int\:\frac{5}{4+9x^{2}}dx
(\partial)/(\partial y)(sqrt(x^2+6xy+y^4))	\frac{\partial\:}{\partial\:y}(\sqrt{x^{2}+6xy+y^{4}})
integral of (22x)/(sqrt(1-x^4))	\int\:\frac{22x}{\sqrt{1-x^{4}}}dx
integral of 8/(x(ln(x))^2)	\int\:\frac{8}{x(\ln(x))^{2}}dx
tangent of f(x)=2x^2-x-3,\at x=-1	tangent\:f(x)=2x^{2}-x-3,\at\:x=-1
derivative of ((2x^2-3x+1^2)/4+2)	\frac{d}{dx}(\frac{(2x^{2}-3x+1)^{2}}{4}+2)
integral of sin^3(θ)cos(θ)	\int\:\sin^{3}(θ)\cos(θ)dθ
integral from 6 to 8 of x/(x^2+4x+20)	\int\:_{6}^{8}\frac{x}{x^{2}+4x+20}dx
(\partial)/(\partial x)(3x^2-27)	\frac{\partial\:}{\partial\:x}(3x^{2}-27)
limit as x approaches 0+of x(ln(x))^2	\lim\:_{x\to\:0+}(x(\ln(x))^{2})
derivative of ((-4x(2x-2))/(-3x^2+1))	\frac{d}{dx}(\frac{(-4x)(2x-2)}{-3x^{2}+1})
limit as x approaches-1 of x-x^3	\lim\:_{x\to\:-1}(x-x^{3})
derivative of (xy^3+x^2y^3)	\frac{d}{dx}((xy^{3}+x^{2}y)^{3})
y^'+3ty=t	y^{\prime\:}+3ty=t
integral of sqrt(108+36x^2)	\int\:\sqrt{108+36x^{2}}dx
integral of 1/(9x+7)	\int\:\frac{1}{9x+7}dx
derivative of 1/(3(x-1^{2/3)})	\frac{d}{dx}(\frac{1}{3(x-1)^{\frac{2}{3}}})
integral of (9/x-4/(x^3))	\int\:(\frac{9}{x}-\frac{4}{x^{3}})dx
d/(dθ)(cos(θ)-sin(θ))	\frac{d}{dθ}(\cos(θ)-\sin(θ))
implicit (dy)/(dx),y^3=x^4	implicit\:\frac{dy}{dx},y^{3}=x^{4}
(\partial)/(\partial x)(x/y+e^y)	\frac{\partial\:}{\partial\:x}(\frac{x}{y}+e^{y})
d/(d{x)}({y}^2{z}(x))	\frac{d}{d{x}}({y}^{2}{z}(x))
sum from n=1 to infinity of n*sin(1/n)	\sum\:_{n=1}^{\infty\:}n\cdot\:\sin(\frac{1}{n})
integral of (x^2)/((36+x^2)^2)	\int\:\frac{x^{2}}{(36+x^{2})^{2}}dx
limit as x approaches 1 of 5(2x+3)^{-1}	\lim\:_{x\to\:1}(5(2x+3)^{-1})
integral of sin(3x)cos(x)	\int\:\sin(3x)\cos(x)dx
y^'-5/x y=(y^5)/(x^{18)},y(1)=1	y^{\prime\:}-\frac{5}{x}y=\frac{y^{5}}{x^{18}},y(1)=1
tangent of y=x^2-9,(2,-5)	tangent\:y=x^{2}-9,(2,-5)
integral of pi/4 x-xarctan(x)	\int\:\frac{π}{4}x-x\arctan(x)dx
integral of cos(8x^2+pi)	\int\:\cos(8x^{2}+π)dx
(d^2)/(dx^2)(csc(x))	\frac{d^{2}}{dx^{2}}(\csc(x))
(\partial)/(\partial x)((-2x)/((1+x^2)^2))	\frac{\partial\:}{\partial\:x}(\frac{-2x}{(1+x^{2})^{2}})
integral of ((x^6+3x^4-2x)/(x^4))	\int\:(\frac{x^{6}+3x^{4}-2x}{x^{4}})dx
(\partial)/(\partial q)((p(q,r)+q)/(p(q,r)+r))	\frac{\partial\:}{\partial\:q}(\frac{p(q,r)+q}{p(q,r)+r})
2x(1+y^2)dx-y(1+2x^2)dy=0	2x(1+y^{2})dx-y(1+2x^{2})dy=0
inverse oflaplace ((2s+1))/((s^2+6s+2))	inverselaplace\:\frac{(2s+1)}{(s^{2}+6s+2)}
area 3x^2,-3x+6,[-4,2]	area\:3x^{2},-3x+6,[-4,2]
integral of 1/(x^4+1)	\int\:\frac{1}{x^{4}+1}dx
limit as x approaches-2 of e^{x+x^2}	\lim\:_{x\to\:-2}(e^{x+x^{2}})
limit as x approaches 0 of x^3(x^4+2x^3)	\lim\:_{x\to\:0}(x^{3}(x^{4}+2x^{3}))
derivative of-sec^2(3-2x)	\frac{d}{dx}(-\sec^{2}(3-2x))
derivative of (2(-3x^4+1)/((x^4+1)^2))	\frac{d}{dx}(\frac{2(-3x^{4}+1)}{(x^{4}+1)^{2}})
derivative of-x^3-2x^2+11x+a	\frac{d}{dx}(-x^{3}-2x^{2}+11x+a)
integral of 2x^3\sqrt[3]{(6x^4-4)^2}	\int\:2x^{3}\sqrt[3]{(6x^{4}-4)^{2}}dx
integral of (e^x)/(6e^x+2)	\int\:\frac{e^{x}}{6e^{x}+2}dx
(\partial)/(\partial x)(-7e^xln(y))	\frac{\partial\:}{\partial\:x}(-7e^{x}\ln(y))
derivative of-4/(x^5)	\frac{d}{dx}(-\frac{4}{x^{5}})
inverse oflaplace 1/(S(S^2+4S+1))	inverselaplace\:\frac{1}{S\cdot\:(S^{2}+4\cdot\:S+1)}
limit as t approaches-1 of t^3	\lim\:_{t\to\:-1}(t^{3})
integral from 0 to 2 of 3x^2	\int\:_{0}^{2}3x^{2}dx
maclaurin 1/2 cos(x/2)	maclaurin\:\frac{1}{2}\cos(\frac{x}{2})
integral of 1/(x(x+2))	\int\:\frac{1}{x(x+2)}dx
derivative of 34e^{x^2}x	\frac{d}{dx}(34e^{x^{2}}x)
integral of 1/(1+x^{1/3)}	\int\:\frac{1}{1+x^{\frac{1}{3}}}dx
laplacetransform t-3	laplacetransform\:t-3
(\partial)/(\partial x)((5x-x^2)(cos(t)))	\frac{\partial\:}{\partial\:x}((5x-x^{2})(\cos(t)))
derivative of f(t)=3t^4-7t^3+2	derivative\:f(t)=3t^{4}-7t^{3}+2
derivative of (pit)/(12)	derivative\:\frac{πt}{12}

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