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Popular Calculus Problems

integral of 1/(sqrt(x^2+14x))	\int\:\frac{1}{\sqrt{x^{2}+14x}}dx
integral of e^{2u}	\int\:e^{2u}du
integral of (2t-3t^2)sqrt(4+36t^2)	\int\:(2t-3t^{2})\sqrt{4+36t^{2}}dt
integral of x*ln(x^2)	\int\:x\cdot\:\ln(x^{2})dx
area x^2,6x-9,y=0	area\:x^{2},6x-9,y=0
y^'-2/x y=(y^3)/(x^3),y(1)=1	y^{\prime\:}-\frac{2}{x}y=\frac{y^{3}}{x^{3}},y(1)=1
tangent of-2/5 x^2,\at x=-1	tangent\:-\frac{2}{5}x^{2},\at\:x=-1
derivative of-(cos(1/x))/(x^2)	derivative\:-\frac{\cos(\frac{1}{x})}{x^{2}}
tangent of y=e^x,(0,1)	tangent\:y=e^{x},(0,1)
derivative of 6/(3x+1)	derivative\:\frac{6}{3x+1}
derivative of (3x^5+9/(x^3))	\frac{d}{dx}(\frac{3x^{5}+9}{x^{3}})
integral of 1/(8x+1)	\int\:\frac{1}{8x+1}dx
limit as x approaches 1+of ln(x-1)	\lim\:_{x\to\:1+}(\ln(x-1))
integral of e^{4x+7}	\int\:e^{4x+7}dx
maclaurin e^x*sin(2x)	maclaurin\:e^{x}\cdot\:\sin(2x)
laplacetransform f(t)=t^2+6t-3	laplacetransform\:f(t)=t^{2}+6t-3
tangent of f(x)=2x^4,(-2,32)	tangent\:f(x)=2x^{4},(-2,32)
integral of (x+3)/(x^2-1)	\int\:\frac{x+3}{x^{2}-1}dx
derivative of 18xe^{x^2}	\frac{d}{dx}(18xe^{x^{2}})
t^2y^{''}-2y=3t^2-1,y(1)= 3/2 ,y^'(1)=3	t^{2}y^{\prime\:\prime\:}-2y=3t^{2}-1,y(1)=\frac{3}{2},y^{\prime\:}(1)=3
inverse oflaplace s/((s+4)^2(s^2-9))	inverselaplace\:\frac{s}{(s+4)^{2}(s^{2}-9)}
integral of (9e^{-9/8 x})/(32)x	\int\:\frac{9e^{-\frac{9}{8}x}}{32}xdx
integral of 3e^x-sin(x)	\int\:3e^{x}-\sin(x)dx
integral from 3 to infinity of e^{-x/5}	\int\:_{3}^{\infty\:}e^{-\frac{x}{5}}dx
integral of (4/(sqrt(1-x^2)))	\int\:(\frac{4}{\sqrt{1-x^{2}}})dx
inverse oflaplace 2/(s^3(s^2+5))	inverselaplace\:\frac{2}{s^{3}(s^{2}+5)}
integral from 0 to 1 of t^3(4+t^4)^3	\int\:_{0}^{1}t^{3}(4+t^{4})^{3}dt
2y^{''}+2y+y=0	2y^{\prime\:\prime\:}+2y+y=0
integral from 1 to 5 of 5x-5/x	\int\:_{1}^{5}5x-\frac{5}{x}dx
integral of (x^5)/((2-x^6)^2)	\int\:\frac{x^{5}}{(2-x^{6})^{2}}dx
(\partial)/(\partial x)(2y-1)	\frac{\partial\:}{\partial\:x}(2y-1)
limit as n approaches infinity of ((cos(1/n)-1))/(1/n)	\lim\:_{n\to\:\infty\:}(\frac{(\cos(\frac{1}{n})-1)}{\frac{1}{n}})
integral of-5t	\int\:-5tdt
derivative of (1-2x/(3+x))	\frac{d}{dx}(\frac{1-2x}{3+x})
derivative of cos(sqrt(x^5))	\frac{d}{dx}(\cos(\sqrt{x^{5}}))
integral of e^{x-e^x}	\int\:e^{x-e^{x}}dx
limit as x approaches 3 of x^2+2x	\lim\:_{x\to\:3}(x^{2}+2x)
integral of (r^2-10r+4)/(r^3)	\int\:\frac{r^{2}-10r+4}{r^{3}}dr
y^'+y=sin(t),y(0)=-1	y^{\prime\:}+y=\sin(t),y(0)=-1
limit as x approaches-6 of (x^2-4)/(6-x)	\lim\:_{x\to\:-6}(\frac{x^{2}-4}{6-x})
integral of 2t-1	\int\:2t-1dt
derivative of 4x+9	derivative\:4x+9
integral of (4x-3)^5	\int\:(4x-3)^{5}dx
integral of cos(nwt)	\int\:\cos(nwt)dt
y^{''}+9y=3sin(3t)	y^{\prime\:\prime\:}+9y=3\sin(3t)
derivative of y=(1-e^x)^4	derivative\:y=(1-e^{x})^{4}
(\partial)/(\partial x)(1/2 mv^2)	\frac{\partial\:}{\partial\:x}(\frac{1}{2}mv^{2})
derivative of y(θ)=2-θ^5sin(θ)	derivative\:y(θ)=2-θ^{5}\sin(θ)
derivative of 500(3+(5t)/(30+t^2))	derivative\:500(3+\frac{5t}{30+t^{2}})
integral of pi(sqrt(y)+2)^2	\int\:π(\sqrt{y}+2)^{2}dy
(\partial)/(\partial y)(x^3+x^2y^3-2y^2)	\frac{\partial\:}{\partial\:y}(x^{3}+x^{2}y^{3}-2y^{2})
(d^2)/(dx^2)(e^{6x})	\frac{d^{2}}{dx^{2}}(e^{6x})
integral of (x^2)/(e^{x^3)}	\int\:\frac{x^{2}}{e^{x^{3}}}dx
derivative of ln(16)	\frac{d}{dx}(\ln(16))
limit as x approaches 6 of (7x-4)/(2x-8)	\lim\:_{x\to\:6}(\frac{7x-4}{2x-8})
integral from 0 to 2 of xe^x	\int\:_{0}^{2}xe^{x}dx
integral of (sqrt(49x^2-100))/(x^3)	\int\:\frac{\sqrt{49x^{2}-100}}{x^{3}}dx
derivative of y=tan(sqrt(x))	derivative\:y=\tan(\sqrt{x})
derivative of cos(x-y)	\frac{d}{dx}(\cos(x-y))
(\partial)/(\partial y)(6y+1/x-x/(y^2))	\frac{\partial\:}{\partial\:y}(6y+\frac{1}{x}-\frac{x}{y^{2}})
derivative of (sqrt(x)/(x+8))	\frac{d}{dx}(\frac{\sqrt{x}}{x+8})
integral of 3-x^2	\int\:3-x^{2}dx
inverse oflaplace 1/(s^2+7s)	inverselaplace\:\frac{1}{s^{2}+7s}
integral of 1+e^{-x}	\int\:1+e^{-x}dx
limit as x approaches 0 of a/x	\lim\:_{x\to\:0}(\frac{a}{x})
sum from n=0 to infinity of (2n)!(x/7)^n	\sum\:_{n=0}^{\infty\:}(2n)!(\frac{x}{7})^{n}
d/(dt)(5ln(t))	\frac{d}{dt}(5\ln(t))
sum from n=0 to infinity of (5/16)^n	\sum\:_{n=0}^{\infty\:}(\frac{5}{16})^{n}
integral of 1/(\sqrt[4]{x)}	\int\:\frac{1}{\sqrt[4]{x}}dx
d/(du)(e^{-u})	\frac{d}{du}(e^{-u})
limit as x approaches 2 of x^2+2x+4	\lim\:_{x\to\:2}(x^{2}+2x+4)
limit as x approaches 1 of x/(1-x)	\lim\:_{x\to\:1}(\frac{x}{1-x})
(\partial)/(\partial x)(x*arctan(y/x))	\frac{\partial\:}{\partial\:x}(x\cdot\:\arctan(\frac{y}{x}))
integral from 0 to 1 of xcos(3pix)	\int\:_{0}^{1}x\cos(3πx)dx
derivative of 5e^{3x}	derivative\:5e^{3x}
limit as n approaches infinity of tan(n)	\lim\:_{n\to\:\infty\:}(\tan(n))
(\partial)/(\partial y)(4xy^2+x^2)	\frac{\partial\:}{\partial\:y}(4xy^{2}+x^{2})
derivative of x^3+2x^4	\frac{d}{dx}(x^{3}+2x^{4})
integral of (x^5)/(sqrt(1-x^6))	\int\:\frac{x^{5}}{\sqrt{1-x^{6}}}dx
derivative of 24x^{1/2}	\frac{d}{dx}(24x^{\frac{1}{2}})
(\partial)/(\partial y)(xe^{y-z})	\frac{\partial\:}{\partial\:y}(xe^{y-z})
derivative of-e^{-x}-e^{-x}x	\frac{d}{dx}(-e^{-x}-e^{-x}x)
(dy)/(dx)=0.0017y(900-y)	\frac{dy}{dx}=0.0017y(900-y)
derivative of cos(e^{-2θ^5})	derivative\:\cos(e^{-2θ^{5}})
(\partial)/(\partial x)(arctan(x+6y))	\frac{\partial\:}{\partial\:x}(\arctan(x+6y))
limit as x approaches infinity of ln(-1)	\lim\:_{x\to\:\infty\:}(\ln(-1))
derivative of (sin(x^3))/x	derivative\:\frac{\sin(x^{3})}{x}
derivative of sqrt(x-\sqrt{y)}	\frac{d}{dx}(\sqrt{x-\sqrt{y}})
laplacetransform 3cos(3t)	laplacetransform\:3\cos(3t)
y^{''}+8y^'+19y=0,y(0)=3,y^'(0)=-4	y^{\prime\:\prime\:}+8y^{\prime\:}+19y=0,y(0)=3,y^{\prime\:}(0)=-4
y^{'''}-2y^{''}-12y^'+16y=0	y^{\prime\:\prime\:\prime\:}-2y^{\prime\:\prime\:}-12y^{\prime\:}+16y=0
limit as x approaches-3+of-2/(x^2-9)	\lim\:_{x\to\:-3+}(-\frac{2}{x^{2}-9})
inverse oflaplace 3/((2s^2+8s+10))	inverselaplace\:\frac{3}{(2s^{2}+8s+10)}
integral of 1/(x^2-8x+1)	\int\:\frac{1}{x^{2}-8x+1}dx
integral of (e^y)/y	\int\:\frac{e^{y}}{y}dy
integral of 22x^2ln(x)	\int\:22x^{2}\ln(x)dx
derivative of g(x)=x^2	derivative\:g(x)=x^{2}
limit as x approaches 0 of In(1+sin(x))	\lim\:_{x\to\:0}(In(1+\sin(x)))
derivative of (x^3+2/x)	\frac{d}{dx}(\frac{x^{3}+2}{x})
derivative of \sqrt[3]{10x+5}	\frac{d}{dx}(\sqrt[3]{10x+5})

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