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Popular Calculus Problems

integral from 1 to 5 of sqrt(5)	\int\:_{1}^{5}\sqrt{5}dx
limit as x approaches 0+of x^3	\lim\:_{x\to\:0+}(x^{3})
inverse oflaplace s/((s+2)(s^2+4))	inverselaplace\:\frac{s}{(s+2)(s^{2}+4)}
integral of (sqrt(x)+\sqrt[3]{x})	\int\:(\sqrt{x}+\sqrt[3]{x})dx
limit as x approaches 2 of x^2-7x+2	\lim\:_{x\to\:2}(x^{2}-7x+2)
tangent of f(x)=3x^3+8x^2,\at x=-2	tangent\:f(x)=3x^{3}+8x^{2},\at\:x=-2
limit as x approaches 5 of 7/(x-5)	\lim\:_{x\to\:5}(\frac{7}{x-5})
limit as x approaches infinity of 7+4/x	\lim\:_{x\to\:\infty\:}(7+\frac{4}{x})
sum from n=1 to infinity of (3n)/(2n+1)	\sum\:_{n=1}^{\infty\:}\frac{3n}{2n+1}
(\partial)/(\partial x)(y/(x^2+y^2+1))	\frac{\partial\:}{\partial\:x}(\frac{y}{x^{2}+y^{2}+1})
(\partial)/(\partial v)(u^2)	\frac{\partial\:}{\partial\:v}(u^{2})
(\partial)/(\partial x)(y+x^2)	\frac{\partial\:}{\partial\:x}(y+x^{2})
xy^'+2y=-4x	xy^{\prime\:}+2y=-4x
derivative of (x^3^5)	\frac{d}{dx}((x^{3})^{5})
sum from n=0 to infinity of 1+1/n	\sum\:_{n=0}^{\infty\:}1+\frac{1}{n}
y^'-y/x =x	y^{\prime\:}-\frac{y}{x}=x
derivative of-5e^{-x}	\frac{d}{dx}(-5e^{-x})
integral of 1/(sqrt(8x+1))	\int\:\frac{1}{\sqrt{8x+1}}dx
integral of (5x^2-x-3)/(x^2(x+1))	\int\:\frac{5x^{2}-x-3}{x^{2}(x+1)}dx
integral of ((cos(2x)-1))/(cos(2x)+1)	\int\:\frac{(\cos(2x)-1)}{\cos(2x)+1}dx
integral of xy	\int\:xydx
slope of (7,-7),(5,-3)	slope\:(7,-7),(5,-3)
limit as h approaches 0 of ((cos(x+h)-cos(x)))/h	\lim\:_{h\to\:0}(\frac{(\cos(x+h)-\cos(x))}{h})
sum from n=0 to infinity of 3x^{2n+1}	\sum\:_{n=0}^{\infty\:}3x^{2n+1}
y^'=(e^x-e^{-x})/(3+4y)	y^{\prime\:}=\frac{e^{x}-e^{-x}}{3+4y}
integral of e^{-αx}	\int\:e^{-αx}dx
ty^'+4y=t^2-t+7	ty^{\prime\:}+4y=t^{2}-t+7
laplacetransform t^2sin^2(t)	laplacetransform\:t^{2}\sin^{2}(t)
(d^2)/(dx^2)(sin(3x))	\frac{d^{2}}{dx^{2}}(\sin(3x))
integral of 3sin^3(xco)s^7x	\int\:3\sin^{3}(xco)s^{7}xdx
limit as x approaches 3-of x/(x^2-9)	\lim\:_{x\to\:3-}(\frac{x}{x^{2}-9})
derivative of (2-x(y-2)(3-x-y))	\frac{d}{dx}((2-x)(y-2)(3-x-y))
limit as x approaches infinity of x/8	\lim\:_{x\to\:\infty\:}(\frac{x}{8})
limit as x approaches 0+of (x^2)/3-3/x	\lim\:_{x\to\:0+}(\frac{x^{2}}{3}-\frac{3}{x})
(\partial)/(\partial x)(xe^{2x})	\frac{\partial\:}{\partial\:x}(xe^{2x})
(\partial)/(\partial x)(4x^3y^3-3)	\frac{\partial\:}{\partial\:x}(4x^{3}y^{3}-3)
tangent of y=(e^{-x})/(x+1),\at x=1	tangent\:y=\frac{e^{-x}}{x+1},\at\:x=1
implicit (dy)/(dx),y=e^x	implicit\:\frac{dy}{dx},y=e^{x}
(dy)/(dt)-(2t)/(1+t^2)y=3	\frac{dy}{dt}-\frac{2t}{1+t^{2}}y=3
derivative of tan^2(y)	derivative\:\tan^{2}(y)
(\partial)/(\partial x)(2x^3+3y^2-5xy)	\frac{\partial\:}{\partial\:x}(2x^{3}+3y^{2}-5xy)
integral of (2x)/((x-1)^2)	\int\:\frac{2x}{(x-1)^{2}}dx
integral from-pi to pi of sin^{101}(x)	\int\:_{-π}^{π}\sin^{101}(x)dx
derivative of sec(5x+2)	\frac{d}{dx}(\sec(5x+2))
(\partial)/(\partial x)(e^{x^2+y^2+2y+5})	\frac{\partial\:}{\partial\:x}(e^{x^{2}+y^{2}+2y+5})
limit as x approaches 0 of x^2-8x+9	\lim\:_{x\to\:0}(x^{2}-8x+9)
laplacetransform e^6	laplacetransform\:e^{6}
integral from 7 to infinity of 2/(x^3)	\int\:_{7}^{\infty\:}\frac{2}{x^{3}}dx
derivative of 8-2/3 x	\frac{d}{dx}(8-\frac{2}{3}x)
y^'-((2x)/(1+x^2))y=1	y^{\prime\:}-(\frac{2x}{1+x^{2}})y=1
integral of x^{4n+2}	\int\:x^{4n+2}dx
(x-3)e^{(-2y)}=(dy)/(dx)	(x-3)e^{(-2y)}=\frac{dy}{dx}
derivative of f(x)=ln(sqrt(x(1-x)))	derivative\:f(x)=\ln(\sqrt{x(1-x)})
integral of 1/(x(x^4-1))	\int\:\frac{1}{x(x^{4}-1)}dx
derivative of (sqrt(7))/(x^6)	derivative\:\frac{\sqrt{7}}{x^{6}}
3(1+x^2)(dy)/(dx)=2xy^4	3(1+x^{2})\frac{dy}{dx}=2xy^{4}
integral of 1/(sqrt(4-9x^2))	\int\:\frac{1}{\sqrt{4-9x^{2}}}dx
limit as x approaches 3 of 6-2x	\lim\:_{x\to\:3}(6-2x)
limit as x approaches i of x^2+2x	\lim\:_{x\to\:i}(x^{2}+2x)
integral of (sqrt(1-\sqrt{x)})/(sqrt(x))	\int\:\frac{\sqrt{1-\sqrt{x}}}{\sqrt{x}}dx
integral of-(2xy)/((x^2+y^2)^2)	\int\:-\frac{2xy}{(x^{2}+y^{2})^{2}}dy
derivative of x+ln\|x^2-4x+3\|	\frac{d}{dx}(x+\ln\left\|x^{2}-4x+3\right\|)
derivative of cos((sqrt(3))/2 x)	derivative\:\cos(\frac{\sqrt{3}}{2}x)
derivative of ln(sqrt(x^2+19))	\frac{d}{dx}(\ln(\sqrt{x^{2}+19}))
tangent of f(x)=sqrt(5x+6),\at a=2	tangent\:f(x)=\sqrt{5x+6},\at\:a=2
2x^2-80x+y^2+49=0(0)	2x^{2}-80x+y^{2}+49=0(0)
integral from 1 to 2 of 4-x^2	\int\:_{1}^{2}4-x^{2}dx
limit as (x,x^5) approaches (0,0) of (x^5y)/(x^{10)+y^5}	\lim\:_{(x,x^{5})\to\:(0,0)}(\frac{x^{5}y}{x^{10}+y^{5}})
limit as x approaches 2-of (6x)/(x-2)	\lim\:_{x\to\:2-}(\frac{6x}{x-2})
integral of (ke^{-kx})	\int\:(ke^{-kx})dx
y^'+3(tan(3x))y=cos(3x)	y^{\prime\:}+3(\tan(3x))y=\cos(3x)
integral of (2x-3)e^{x^2-3x}	\int\:(2x-3)e^{x^{2}-3x}dx
(\partial)/(\partial x)(x^5y)	\frac{\partial\:}{\partial\:x}(x^{5}y)
integral of (4x^2+2x+8)/(x(x^2+2)^2)	\int\:\frac{4x^{2}+2x+8}{x(x^{2}+2)^{2}}dx
limit as x approaches+1 of-3/(x-1)	\lim\:_{x\to\:+1}(-\frac{3}{x-1})
y^'=2y+xe^x,y(0)=-1	y^{\prime\:}=2y+xe^{x},y(0)=-1
(\partial)/(\partial y)(xy+ln(x+y))	\frac{\partial\:}{\partial\:y}(xy+\ln(x+y))
maclaurin cos(pix)	maclaurin\:\cos(πx)
(dy)/(dx)+ycos(x)=3cos(x),y(0)=5	\frac{dy}{dx}+y\cos(x)=3\cos(x),y(0)=5
area y=4x-x^2,y=x	area\:y=4x-x^{2},y=x
(dx)/(dt)+8x=0	\frac{dx}{dt}+8x=0
derivative of 4x(sin(x+cos(x)))	\frac{d}{dx}(4x(\sin(x)+\cos(x)))
(dy)/(dx)=(x-1)/(y^3)	\frac{dy}{dx}=\frac{x-1}{y^{3}}
integral of ((ln(x))^{32})/x	\int\:\frac{(\ln(x))^{32}}{x}dx
limit as x approaches 2 of 2x^4-10	\lim\:_{x\to\:2}(2x^{4}-10)
(d^2)/(dx^2)(ln(x^2+3x+15))	\frac{d^{2}}{dx^{2}}(\ln(x^{2}+3x+15))
f(x)=8ln(x)	f(x)=8\ln(x)
limit as x approaches 1 of 3x^2-7x+1	\lim\:_{x\to\:1}(3x^{2}-7x+1)
derivative of x^3-6x^2+8x	\frac{d}{dx}(x^{3}-6x^{2}+8x)
integral of (7x^2)ex^3+1	\int\:(7x^{2})ex^{3}+1dx
f(x)=-4sin(4x)	f(x)=-4\sin(4x)
tangent of y=x+6/x ,(3,5)	tangent\:y=x+\frac{6}{x},(3,5)
81y^{''}+180y^'+125y=0,y(3)=6,y^'(3)=6	81y^{\prime\:\prime\:}+180y^{\prime\:}+125y=0,y(3)=6,y^{\prime\:}(3)=6
derivative of 8cos^2(x)	\frac{d}{dx}(8\cos^{2}(x))
area 2x^3-6x^2-2x+6,-x^3+3x^2+x-3	area\:2x^{3}-6x^{2}-2x+6,-x^{3}+3x^{2}+x-3
integral from 0 to 4 of pi((20-5x)/4)^2	\int\:_{0}^{4}π(\frac{20-5x}{4})^{2}dx
derivative of y=4x^2+1	derivative\:y=4x^{2}+1
integral of 2x^3e^{x^2}	\int\:2x^{3}e^{x^{2}}dx
integral of (1/(2sqrt(x)))	\int\:(\frac{1}{2\sqrt{x}})dx
area y=sqrt(3x),x=0,x=4	area\:y=\sqrt{3x},x=0,x=4

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