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Popular Calculus Problems

integral from 1 to 5 of x/(sqrt(5-x))	\int\:_{1}^{5}\frac{x}{\sqrt{5-x}}dx
laplacetransform 9/4 t^2e^{2t}e^{3t}	laplacetransform\:\frac{9}{4}t^{2}e^{2t}e^{3t}
t^2((dy)/(dt))+y^2=ty	t^{2}(\frac{dy}{dt})+y^{2}=ty
derivative of xtan(2sqrt(x)+7)	\frac{d}{dx}(x\tan(2\sqrt{x})+7)
derivative of 2x^2+4x-5	derivative\:2x^{2}+4x-5
sum from n=0 to infinity of 3*(-1/5)^n	\sum\:_{n=0}^{\infty\:}3\cdot\:(-\frac{1}{5})^{n}
t^2y^{''}+19ty^'+85y=0	t^{2}y^{\prime\:\prime\:}+19ty^{\prime\:}+85y=0
integral of-1/64 e^{-4x}	\int\:-\frac{1}{64}e^{-4x}dx
y^'=e^{2y}sin(3x)	y^{\prime\:}=e^{2y}\sin(3x)
y^'=(3sec(y))/((x+1)^2)	y^{\prime\:}=\frac{3\sec(y)}{(x+1)^{2}}
integral of (3x-1x-7ex+14e)	\int\:(3x-1x-7ex+14e)dx
integral of cos^2(x/2)	\int\:\cos^{2}(\frac{x}{2})dx
limit as x approaches 3 of 2x^2-7x+6	\lim\:_{x\to\:3}(2x^{2}-7x+6)
derivative of n/(x+1)	\frac{d}{dx}(\frac{n}{x+1})
integral of 1/(sqrt(x)*\sqrt{1-x)}	\int\:\frac{1}{\sqrt{x}\cdot\:\sqrt{1-x}}dx
tangent of 1/((x-1))	tangent\:\frac{1}{(x-1)}
taylor sin(x), pi/4	taylor\:\sin(x),\frac{π}{4}
y^{''}+6y^'+8y=4sin(2t)	y^{\prime\:\prime\:}+6y^{\prime\:}+8y=4\sin(2t)
integral from 1 to 3 of sqrt(x-1)	\int\:_{1}^{3}\sqrt{x-1}dx
(dy)/(dx)=(e^{x-y})/(1+e^x)	\frac{dy}{dx}=\frac{e^{x-y}}{1+e^{x}}
integral of (1+4x)^{-1/2}	\int\:(1+4x)^{-\frac{1}{2}}dx
integral of (x^2+1)/((x-7)(x-6)^2)	\int\:\frac{x^{2}+1}{(x-7)(x-6)^{2}}dx
derivative of \sqrt[3]{(9x^5+4^2})	\frac{d}{dx}(\sqrt[3]{(9x^{5}+4)^{2}})
integral from 1 to 2 of 3/(e^{4t)}	\int\:_{1}^{2}\frac{3}{e^{4t}}dt
y^'=-0.5y+x	y^{\prime\:}=-0.5y+x
integral of x^4sin(x)	\int\:x^{4}\sin(x)dx
integral of y/2	\int\:\frac{y}{2}dy
derivative of f(x)=5xsqrt(2)	derivative\:f(x)=5x\sqrt{2}
derivative of \sqrt[5]{(5x)/(8x-3)}	derivative\:\sqrt[5]{\frac{5x}{8x-3}}
inverse oflaplace [1]	inverselaplace\:[1]
integral of 17(tan(x))(ln(cos(x)))	\int\:17(\tan(x))(\ln(\cos(x)))dx
f(t)=4sin(t)	f(t)=4\sin(t)
integral of 9/(16+25r^2)	\int\:\frac{9}{16+25r^{2}}dr
(dy)/(dt)-y=e^t+12e^{7t}	\frac{dy}{dt}-y=e^{t}+12e^{7t}
derivative of (x+2(3x^2-4)^2)	\frac{d}{dx}((x+2)(3x^{2}-4)^{2})
taylor x^4+2x	taylor\:x^{4}+2x
(\partial)/(\partial x)(ln(x^y)+ln(y^x))	\frac{\partial\:}{\partial\:x}(\ln(x^{y})+\ln(y^{x}))
derivative of cos(3x3)	\frac{d}{dx}(\cos(3x)3)
tangent of f(x)=x^2-x,\at x=-1	tangent\:f(x)=x^{2}-x,\at\:x=-1
integral of (a^2+x^2)^{1/2}	\int\:(a^{2}+x^{2})^{\frac{1}{2}}dx
y^{''}-8y^'+9y=xe^x	y^{\prime\:\prime\:}-8y^{\prime\:}+9y=xe^{x}
laplacetransform sin(2(t-pi/2))	laplacetransform\:\sin(2(t-\frac{π}{2}))
area x^2-4x,x-4	area\:x^{2}-4x,x-4
(\partial)/(\partial y)(sqrt(2x^2-5y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{2x^{2}-5y^{2}})
y^{''}+4y=-16sin(2t)	y^{\prime\:\prime\:}+4y=-16\sin(2t)
4x^2((dy)/(dx))=((dy)/(dx))+6xe^{-y}	4x^{2}(\frac{dy}{dx})=(\frac{dy}{dx})+6xe^{-y}
limit as x approaches infinity of 4-5x	\lim\:_{x\to\:\infty\:}(4-5x)
integral of sin(9pix)	\int\:\sin(9πx)dx
integral of (x^3e^{x^2})	\int\:(x^{3}e^{x^{2}})dx
y^{''}+16y=4csc^2(4t)	y^{\prime\:\prime\:}+16y=4\csc^{2}(4t)
derivative of (x^4+1^{1/4})	\frac{d}{dx}((x^{4}+1)^{\frac{1}{4}})
derivative of (3x^4+7/(x^2))	\frac{d}{dx}(\frac{3x^{4}+7}{x^{2}})
limit as x approaches 0 of 8	\lim\:_{x\to\:0}(8)
integral of 2x(x^2+6)^6	\int\:2x(x^{2}+6)^{6}dx
limit as x approaches-0.2 of 12.1951	\lim\:_{x\to\:-0.2}(12.1951)
maclaurin e^{e^x}	maclaurin\:e^{e^{x}}
t^2y^{''}+ty^'+81y=0	t^{2}y^{\prime\:\prime\:}+ty^{\prime\:}+81y=0
(\partial)/(\partial y)(x+sin(y))	\frac{\partial\:}{\partial\:y}(x+\sin(y))
limit as x approaches 0 of (e^x-1)/(x^7)	\lim\:_{x\to\:0}(\frac{e^{x}-1}{x^{7}})
limit as R approaches 1+of 1/(R-1)	\lim\:_{R\to\:1+}(\frac{1}{R-1})
area 2/x ,8x, 1/(8x)	area\:\frac{2}{x},8x,\frac{1}{8x}
integral of (3x-3)e^{3x^2-6x}	\int\:(3x-3)e^{3x^{2}-6x}dx
derivative of y=17^x	derivative\:y=17^{x}
sum from n=1 to infinity}((-1)^{3n of)/n	\sum\:_{n=1}^{\infty\:}\frac{(-1)^{3n}}{n}
derivative of f(x)=(6x)/(sqrt(6x^2+5))	derivative\:f(x)=\frac{6x}{\sqrt{6x^{2}+5}}
(\partial)/(\partial x)(sin(pi(6x-5y)))	\frac{\partial\:}{\partial\:x}(\sin(π(6x-5y)))
x+(sin(y))/(cos(x))y^'=0	x+\frac{\sin(y)}{\cos(x)}y^{\prime\:}=0
derivative of (e^x+e^{-x})/6	derivative\:\frac{e^{x}+e^{-x}}{6}
derivative of f(x)= 3/((x^2-5x)^2)	derivative\:f(x)=\frac{3}{(x^{2}-5x)^{2}}
limit as x approaches 0 of (x^{2/3})/x	\lim\:_{x\to\:0}(\frac{x^{\frac{2}{3}}}{x})
tangent of f(x)=tan^2(x),\at x= pi/4	tangent\:f(x)=\tan^{2}(x),\at\:x=\frac{π}{4}
derivative of (sin(x))/(3x)	derivative\:\frac{\sin(x)}{3x}
maclaurin-log_{e}(1-x)	maclaurin\:-\log_{e}(1-x)
derivative of y=1cos(2)(x)	derivative\:y=1\cos(2)(x)
taylor e^{t^2}	taylor\:e^{t^{2}}
y^{''}+2y^'+y=18e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=18e^{-t}
integral of e^xsec^2(e^x)	\int\:e^{x}\sec^{2}(e^{x})dx
y^{''}+25y=20sin(5x)	y^{\prime\:\prime\:}+25y=20\sin(5x)
e^{x-y}dx+e^{y-x}dy=0	e^{x-y}dx+e^{y-x}dy=0
area y=2(x+1),y=3(x+1),x=4	area\:y=2(x+1),y=3(x+1),x=4
derivative of f(x^2)	derivative\:f(x^{2})
(\partial)/(\partial x)(1/(e^x))	\frac{\partial\:}{\partial\:x}(\frac{1}{e^{x}})
9x-4ysqrt(x^2+1)(dy)/(dx)=0	9x-4y\sqrt{x^{2}+1}\frac{dy}{dx}=0
derivative of \sqrt[4]{sin^3(5x})	\frac{d}{dx}(\sqrt[4]{\sin^{3}(5x)})
tangent of 6/((4x+1))	tangent\:\frac{6}{(4x+1)}
area e^{-x},0,1	area\:e^{-x},0,1
sum from n=1 to infinity of \sqrt[n]{21}	\sum\:_{n=1}^{\infty\:}\sqrt[n]{21}
integral of (x^2+4)^{-1}	\int\:(x^{2}+4)^{-1}dx
sum from n=1 to infinity of (n-1)/(n4^n)	\sum\:_{n=1}^{\infty\:}\frac{n-1}{n4^{n}}
integral of (24)/(1-cos(6x))	\int\:\frac{24}{1-\cos(6x)}dx
derivative of sin(x)+cos(x)	derivative\:\sin(x)+\cos(x)
integral from 0 to 4 of (1+2sqrt(x))^2	\int\:_{0}^{4}(1+2\sqrt{x})^{2}dx
slope ofintercept (1,2),(3,16)	slopeintercept\:(1,2),(3,16)
sum from n=0 to infinity of (n/(n+10))^n	\sum\:_{n=0}^{\infty\:}(\frac{n}{n+10})^{n}
integral of (((-x^2+8)/2)-((x^2)/2))	\int\:((\frac{-x^{2}+8}{2})-(\frac{x^{2}}{2}))dx
(\partial)/(\partial y)(sin(x+e^y))	\frac{\partial\:}{\partial\:y}(\sin(x+e^{y}))
(\partial)/(\partial x)(5y^{4x})	\frac{\partial\:}{\partial\:x}(5y^{4x})
sum from n=0 to infinity of x^{2n+2}	\sum\:_{n=0}^{\infty\:}x^{2n+2}
derivative of (sqrt(x)+7)(sqrt(x)-4)	derivative\:(\sqrt{x}+7)(\sqrt{x}-4)
(\partial)/(\partial x)(x-sin(x))	\frac{\partial\:}{\partial\:x}(x-\sin(x))

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