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Popular Calculus Problems

integral of (x^3-6x+5)/x	\int\:\frac{x^{3}-6x+5}{x}dx
y^{''}-y=0,y(0)=2,y^'(0)=-2	y^{\prime\:\prime\:}-y=0,y(0)=2,y^{\prime\:}(0)=-2
(\partial)/(\partial x)(xsqrt(x^2+y^2+z^2))	\frac{\partial\:}{\partial\:x}(x\sqrt{x^{2}+y^{2}+z^{2}})
derivative of 2/(4-cos(2x))	\frac{d}{dx}(\frac{2}{4-\cos(2x)})
integral of 1/(tln(t^2))	\int\:\frac{1}{t\ln(t^{2})}dt
integral of (x^3+5)/(sqrt(5x+3))	\int\:\frac{x^{3}+5}{\sqrt{5x+3}}dx
derivative of (100x/(x+1))	\frac{d}{dx}(\frac{100x}{x+1})
integral of (1+e^{2x})sin(3x)	\int\:(1+e^{2x})\sin(3x)dx
integral of xsec(8)x^2tan(8)x^2	\int\:x\sec(8)x^{2}\tan(8)x^{2}dx
derivative of sqrt(tan(3x))	\frac{d}{dx}(\sqrt{\tan(3x)})
derivative of ((8x)/(sqrt(x^2+4)))	\frac{d}{dx}(\frac{(8x)}{\sqrt{x^{2}+4}})
limit as x approaches 0 of (1-e^x)/x	\lim\:_{x\to\:0}(\frac{1-e^{x}}{x})
tangent of f(x)=1-3x^{[2]},\at x=0	tangent\:f(x)=1-3x^{[2]},\at\:x=0
integral of 3/y	\int\:\frac{3}{y}dy
integral from 1 to 3 of (2x^2+3x-2)/x	\int\:_{1}^{3}\frac{2x^{2}+3x-2}{x}dx
(\partial)/(\partial s)(s/t)	\frac{\partial\:}{\partial\:s}(\frac{s}{t})
integral of x/(3x^2-4)	\int\:\frac{x}{3x^{2}-4}dx
integral of-19x^2-2x+8	\int\:-19x^{2}-2x+8dx
(\partial)/(\partial x)(1+x^3+y^3)	\frac{\partial\:}{\partial\:x}(1+x^{3}+y^{3})
derivative of g(x)=-9/((6x+8)^{3/2)}	derivative\:g(x)=-\frac{9}{(6x+8)^{\frac{3}{2}}}
integral of 5^{3x}	\int\:5^{3x}dx
derivative of 3-1/(\sqrt[3]{x}+4/(sqrt(x))-2sqrt(x))	\frac{d}{dx}(3-\frac{1}{\sqrt[3]{x}}+\frac{4}{\sqrt{x}}-2\sqrt{x})
derivative of cos^2(xdx)	\frac{d}{dx}(\cos^{2}(x)dx)
(\partial)/(\partial x)(ln(3+x^2y^2))	\frac{\partial\:}{\partial\:x}(\ln(3+x^{2}y^{2}))
integral of-1/x+C	\int\:-\frac{1}{x}+Cdx
2xy(dy)/(dx)=y^2-x^2	2xy\frac{dy}{dx}=y^{2}-x^{2}
integral of (3x^2+2e^x)	\int\:(3x^{2}+2e^{x})dx
limit as x approaches 0+of (\|xsin(x)\|)/x	\lim\:_{x\to\:0+}(\frac{\left\|x\sin(x)\right\|}{x})
derivative of sin(e^{5x})	\frac{d}{dx}(\sin(e^{5x}))
integral from 1 to e of ln(15x)	\int\:_{1}^{e}\ln(15x)dx
derivative of-(20/((2+x)^2))	\frac{d}{dx}(-\frac{20}{(2+x)^{2}})
derivative of e^x-8/x	derivative\:e^{x}-\frac{8}{x}
derivative of x^4+1	derivative\:x^{4}+1
integral of 1/(x^{1/3)}	\int\:\frac{1}{x^{\frac{1}{3}}}dx
derivative of ln(5/x)	\frac{d}{dx}(\ln(\frac{5}{x}))
y^{''}+2y^'-3y=2x-17	y^{\prime\:\prime\:}+2y^{\prime\:}-3y=2x-17
taylor 1/(cos(x))	taylor\:\frac{1}{\cos(x)}
derivative of 2x-sin(x)	\frac{d}{dx}(2x-\sin(x))
integral from 0 to 2 of 4x^3	\int\:_{0}^{2}4x^{3}dx
expand 3x^4(4-x)^3	expand\:3x^{4}(4-x)^{3}
integral from 1 to 7 of x^{-3}	\int\:_{1}^{7}x^{-3}dx
integral of 6/(1+6x)	\int\:\frac{6}{1+6x}dx
integral of sqrt(81-t^2)	\int\:\sqrt{81-t^{2}}dt
integral of (sin(2x))/(cos(2x))	\int\:\frac{\sin(2x)}{\cos(2x)}dx
integral of 1-2/x	\int\:1-\frac{2}{x}dx
limit as x approaches infinity of-x^2	\lim\:_{x\to\:\infty\:}(-x^{2})
d/(dt)(1+sin(t))	\frac{d}{dt}(1+\sin(t))
integral from 1 to 4 of \sqrt[3]{x}	\int\:_{1}^{4}\sqrt[3]{x}dx
integral of-3/x	\int\:-\frac{3}{x}dx
derivative of (x+3)^2	derivative\:(x+3)^{2}
d/(dy)(x/((x^2+y^2)))	\frac{d}{dy}(\frac{x}{(x^{2}+y^{2})})
sum from n=1 to infinity}((-1)^{n-1 of n^2)/(12^n)	\sum\:_{n=1}^{\infty\:}\frac{(-1)^{n-1}n^{2}}{12^{n}}
simplify (s+3)/((s+3)^2+9)	simplify\:\frac{s+3}{(s+3)^{2}+9}
derivative of xln(-x)	\frac{d}{dx}(x\ln(-x))
limit as x approaches pi of (tan(x))/x	\lim\:_{x\to\:π}(\frac{\tan(x)}{x})
integral from 7 to infinity of xe^{-5x}	\int\:_{7}^{\infty\:}xe^{-5x}dx
derivative of 4x^3-102x^2+840x+520	\frac{d}{dx}(4x^{3}-102x^{2}+840x+520)
y^{''}+5y^'+6y=1+2t+3t^2	y^{\prime\:\prime\:}+5y^{\prime\:}+6y=1+2t+3t^{2}
simplify 25(x^2-y^2)	simplify\:25(x^{2}-y^{2})
derivative of tan(3x)	derivative\:\tan(3x)
derivative of (5x)/(x+3)	derivative\:\frac{5x}{x+3}
inverse oflaplace 1/(s^3+s^2+5s)	inverselaplace\:\frac{1}{s^{3}+s^{2}+5s}
(dP)/(dt)=2sqrt(Pt)	\frac{dP}{dt}=2\sqrt{Pt}
integral of 24x^3-18x^2+10x	\int\:24x^{3}-18x^{2}+10xdx
integral of x/(sqrt(x-6))	\int\:\frac{x}{\sqrt{x-6}}dx
integral of sin^3(θ)cos^8(θ)	\int\:\sin^{3}(θ)\cos^{8}(θ)dθ
limit as t approaches 0 of (e^t-1)/(t^3)	\lim\:_{t\to\:0}(\frac{e^{t}-1}{t^{3}})
derivative of 2x^3+3x^2-12x	\frac{d}{dx}(2x^{3}+3x^{2}-12x)
tangent of 5x^2-6x+1	tangent\:5x^{2}-6x+1
derivative of f(x)=9sqrt(x)sin(x)	derivative\:f(x)=9\sqrt{x}\sin(x)
tangent of f(x)=e^{-5x},\at x=0	tangent\:f(x)=e^{-5x},\at\:x=0
d/(ds)((s^2-8s+15)/(s^2+3s+2))	\frac{d}{ds}(\frac{s^{2}-8s+15}{s^{2}+3s+2})
2yy^'+4=y^2+4x	2yy^{\prime\:}+4=y^{2}+4x
derivative of x(7x+3)^{1/3}	derivative\:x(7x+3)^{\frac{1}{3}}
integral from 0 to 1 of x^3(1+x^4)^3	\int\:_{0}^{1}x^{3}(1+x^{4})^{3}dx
derivative of ln(sqrt(x+2))	derivative\:\ln(\sqrt{x+2})
integral of y^2e^{y^3}	\int\:y^{2}e^{y^{3}}dy
integral of xe^{x/(10)}	\int\:xe^{\frac{x}{10}}dx
derivative of y=x^{18}	derivative\:y=x^{18}
derivative of x-2sqrt(x)+2ln(sqrt(x+1))	\frac{d}{dx}(x-2\sqrt{x}+2\ln(\sqrt{x+1}))
tangent of y= 5/(sqrt(x-2)),(3,5)	tangent\:y=\frac{5}{\sqrt{x-2}},(3,5)
integral from 0 to 1 of (x^2)/((x+1)^3)	\int\:_{0}^{1}\frac{x^{2}}{(x+1)^{3}}dx
y^'-1/x y=-(y^2)/x	y^{\prime\:}-\frac{1}{x}y=-\frac{y^{2}}{x}
integral of 10m^{-2.3}+5m^{3.6}	\int\:10m^{-2.3}+5m^{3.6}dm
integral of 1/(u^2-1)	\int\:\frac{1}{u^{2}-1}du
derivative of sqrt(x)*5x^2	derivative\:\sqrt{x}\cdot\:5x^{2}
integral of 1/(1+cos^2(θ))	\int\:\frac{1}{1+\cos^{2}(θ)}dθ
derivative of arccos(sin(x^2+9x))	\frac{d}{dx}(\arccos(\sin(x^{2}+9x)))
derivative of f(x)=sqrt(3x+4)	derivative\:f(x)=\sqrt{3x+4}
limit as x approaches 0 of (1+3/x)^x	\lim\:_{x\to\:0}((1+\frac{3}{x})^{x})
tangent of f(x)= 2/(4-x),\at x=1	tangent\:f(x)=\frac{2}{4-x},\at\:x=1
integral from 0 to 1 of cos((pit)/2)	\int\:_{0}^{1}\cos(\frac{πt}{2})dt
limit as x approaches infinity of e^{-s(x)}	\lim\:_{x\to\:\infty\:}(e^{-s(x)})
integral of sqrt(2x+1)-xe^{x^2}	\int\:\sqrt{2x+1}-xe^{x^{2}}dx
derivative of (x-2^{-1})	\frac{d}{dx}((x-2)^{-1})
(d^2)/(dx^2)(7e^{-x^2})	\frac{d^{2}}{dx^{2}}(7e^{-x^{2}})
integral of (x^2+2x+1)/2 sin(1.3x)	\int\:\frac{x^{2}+2x+1}{2}\sin(1.3x)dx
integral from 1 to e^3 of x^4ln(x)	\int\:_{1}^{e^{3}}x^{4}\ln(x)dx
derivative of f(x)=ln(xe^{sqrt(x)}+8)	derivative\:f(x)=\ln(xe^{\sqrt{x}}+8)
implicit 7x^2-y^2=4	implicit\:7x^{2}-y^{2}=4

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