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Popular Calculus Problems

limit as x approaches 2-of csc((pix)/2)	\lim\:_{x\to\:2-}(\csc(\frac{πx}{2}))
integral of (x-2)^{-2}	\int\:(x-2)^{-2}dx
y^{''}+y=1	y^{\prime\:\prime\:}+y=1
maclaurin f(x)=sin(x)	maclaurin\:f(x)=\sin(x)
integral of 81e^{-9x}sin(9x)	\int\:81e^{-9x}\sin(9x)dx
derivative of (\sqrt[3]{x}/(x-6))	\frac{d}{dx}(\frac{\sqrt[3]{x}}{x-6})
derivative of-4+e^{1/(2-x})	\frac{d}{dx}(-4+e^{\frac{1}{2-x}})
area 20-(e^x)^2,(e^x)^2,[0,0.5ln(10)]	area\:20-(e^{x})^{2},(e^{x})^{2},[0,0.5\ln(10)]
(\partial)/(\partial x)(ln(x^2+9y^2+6))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+9y^{2}+6))
integral from 0 to 1 of 24(e^{1/x})/(x^3)	\int\:_{0}^{1}24\frac{e^{\frac{1}{x}}}{x^{3}}dx
limit as x approaches 0 of e^{(-1)/x}	\lim\:_{x\to\:0}(e^{\frac{-1}{x}})
integral of (x^2)/((3-x^3)^2)	\int\:\frac{x^{2}}{(3-x^{3})^{2}}dx
derivative of 5(-csc^2(x+sec^2(x)))	\frac{d}{dx}(5(-\csc^{2}(x)+\sec^{2}(x)))
integral of xcsc(2x)cot(2x)	\int\:x\csc(2x)\cot(2x)dx
integral of 1/((25+x^2)^2)	\int\:\frac{1}{(25+x^{2})^{2}}dx
area f(x)=x^2,g(x)=3x	area\:f(x)=x^{2},g(x)=3x
integral of 3-1/(x^2)	\int\:3-\frac{1}{x^{2}}dx
(\partial)/(\partial y)(x^2+4y^2-800)	\frac{\partial\:}{\partial\:y}(x^{2}+4y^{2}-800)
derivative of 8/(3x^4)	derivative\:\frac{8}{3x^{4}}
integral of sqrt(3x-6)	\int\:\sqrt{3x-6}dx
integral from 0 to 1 of x^3ln(x)	\int\:_{0}^{1}x^{3}\ln(x)dx
(\partial)/(\partial x)(x^3+2(5-5x^2)^2+2)	\frac{\partial\:}{\partial\:x}(x^{3}+2(5-5x^{2})^{2}+2)
(\partial)/(\partial x)(e^{3xy})	\frac{\partial\:}{\partial\:x}(e^{3xy})
integral of (ln(10x))/x	\int\:\frac{\ln(10x)}{x}dx
derivative of In((sqrt(4+x^2)/x))	\frac{d}{dx}(In(\frac{\sqrt{4+x^{2}}}{x}))
integral of (sin(5x))/(cos(5x))	\int\:\frac{\sin(5x)}{\cos(5x)}dx
area 6x,4x^2	area\:6x,4x^{2}
integral of ((sqrt(x)+1)^3)/(sqrt(x))	\int\:\frac{(\sqrt{x}+1)^{3}}{\sqrt{x}}dx
(dy)/(dx)=y,y(0)=1	\frac{dy}{dx}=y,y(0)=1
(dy)/(dx)=8x^4(6+y^2)^{3/2}	\frac{dy}{dx}=8x^{4}(6+y^{2})^{\frac{3}{2}}
limit as x approaches 0 of (e^x-1)/(5x)	\lim\:_{x\to\:0}(\frac{e^{x}-1}{5x})
y^{''}-2y^'+y=3e^x	y^{\prime\:\prime\:}-2y^{\prime\:}+y=3e^{x}
integral of (9sqrt(x))/(x^3+1)	\int\:\frac{9\sqrt{x}}{x^{3}+1}dx
(\partial)/(\partial x)(2-(x^2+y^2)^{1/7})	\frac{\partial\:}{\partial\:x}(2-(x^{2}+y^{2})^{\frac{1}{7}})
derivative of y=(x^5-1)^3	derivative\:y=(x^{5}-1)^{3}
limit as x approaches 0 of xsin(1/(\|x\|))	\lim\:_{x\to\:0}(x\sin(\frac{1}{\left\|x\right\|}))
derivative of-2e^{-x^2}x	derivative\:-2e^{-x^{2}}x
integral of 1/(1-x^3)	\int\:\frac{1}{1-x^{3}}dx
(dy)/(dx)=((2x(y-2)))/(x^2+1)	\frac{dy}{dx}=\frac{(2x(y-2))}{x^{2}+1}
integral from 0 to 2 of x^3-3x^2+2x	\int\:_{0}^{2}x^{3}-3x^{2}+2xdx
tangent of x^2-5x+5	tangent\:x^{2}-5x+5
integral of x^3sqrt(x^2+8)	\int\:x^{3}\sqrt{x^{2}+8}dx
derivative of 1/(arctan(x^2))	\frac{d}{dx}(\frac{1}{\arctan(x^{2})})
integral of cos^2(x)	\int\:\cos^{2}(x)dx
(1+cos(t))(dy)/(dt)=(1+e^{-y})sin(t)	(1+\cos(t))\frac{dy}{dt}=(1+e^{-y})\sin(t)
derivative of ((2x+1/(3x-1))^4)	\frac{d}{dx}((\frac{2x+1}{3x-1})^{4})
derivative of 8x^2cos(xcot(x))	\frac{d}{dx}(8x^{2}\cos(x)\cot(x))
derivative of x*e^{-x+1}	derivative\:x\cdot\:e^{-x+1}
slope ofintercept (4,-4),(8,-10)	slopeintercept\:(4,-4),(8,-10)
integral of sqrt((3+x)/(3-x))	\int\:\sqrt{\frac{3+x}{3-x}}dx
x^{''}+x^'+3x=0	x^{\prime\:\prime\:}+x^{\prime\:}+3x=0
integral of (8x^3)/(x-4)	\int\:\frac{8x^{3}}{x-4}dx
derivative of x/(3x+5)	derivative\:\frac{x}{3x+5}
derivative of 1/(\|x\|+1)+1/(\|x-2\|+1)	derivative\:\frac{1}{\left\|x\right\|+1}+\frac{1}{\left\|x-2\right\|+1}
derivative of (4374/(x^2))	\frac{d}{dx}(\frac{4374}{x^{2}})
(\partial)/(\partial x)(5e^{xy+7})	\frac{\partial\:}{\partial\:x}(5e^{xy+7})
integral of (x^5)/(1+x^3)	\int\:\frac{x^{5}}{1+x^{3}}dx
(\partial)/(\partial y)(y/((x+y+z)))	\frac{\partial\:}{\partial\:y}(\frac{y}{(x+y+z)})
integral from-2 to 3 of (31)/(x^4)	\int\:_{-2}^{3}\frac{31}{x^{4}}dx
derivative of sqrt(10)	\frac{d}{dx}(\sqrt{10})
2e^{3x}(dy)/(dx)=-(6x)/(y^2)	2e^{3x}\frac{dy}{dx}=-\frac{6x}{y^{2}}
area 4x,4, 4/x ,0	area\:4x,4,\frac{4}{x},0
integral of 1/(sqrt(4+x-x^2))	\int\:\frac{1}{\sqrt{4+x-x^{2}}}dx
derivative of 4x^2+xy+2y^2	\frac{d}{dx}(4x^{2}+xy+2y^{2})
(\partial)/(\partial x)(x^2+y^2+z^2)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+z^{2})
integral of 1/(13x-2x^2-15)	\int\:\frac{1}{13x-2x^{2}-15}dx
derivative of (3x^5(6x^4+x)^4)	\frac{d}{dx}((3x^{5})(6x^{4}+x)^{4})
derivative of e^{x^2}	derivative\:e^{x^{2}}
derivative of sqrt(5-x)	derivative\:\sqrt{5-x}
derivative of ln(f(x))	derivative\:\ln(f(x))
slope of 1/(x-1)	slope\:\frac{1}{x-1}
integral of 8t^5	\int\:8t^{5}dt
derivative of axcos(x+bxsin(x))	\frac{d}{dx}(ax\cos(x)+bx\sin(x))
implicit (dy)/(dx),y^4=x^7	implicit\:\frac{dy}{dx},y^{4}=x^{7}
sec^2(pi/4)(pi/5)= 1/4 (dx)/(dt)	\sec^{2}(\frac{π}{4})(\frac{π}{5})=\frac{1}{4}\frac{dx}{dt}
limit as x approaches 6+of sqrt(6-x)	\lim\:_{x\to\:6+}(\sqrt{6-x})
(\partial)/(\partial x)((x^2+y^2)^{4/5})	\frac{\partial\:}{\partial\:x}((x^{2}+y^{2})^{\frac{4}{5}})
derivative of 4x^2sin(x)tan(x)	derivative\:4x^{2}\sin(x)\tan(x)
integral from-1 to 1 of x^2-x^3	\int\:_{-1}^{1}x^{2}-x^{3}dx
integral of (3x)/(sqrt(4x^2+5))	\int\:\frac{3x}{\sqrt{4x^{2}+5}}dx
(8x+9y)dx+(9x+6y)dy=0	(8x+9y)dx+(9x+6y)dy=0
derivative of 2x-2	\frac{d}{dx}(2x-2)
(x+1)y^'+(x+2)y=2xe^{-ax}	(x+1)y^{\prime\:}+(x+2)y=2xe^{-ax}
integral of ((x-1)/3)^2	\int\:(\frac{x-1}{3})^{2}dx
derivative of x(x^4+8^3)	\frac{d}{dx}(x(x^{4}+8)^{3})
limit as x approaches-3 of ln(x^4-3x+10)	\lim\:_{x\to\:-3}(\ln(x^{4}-3x+10))
integral of (2x+5)/(3x(x+3)^2)	\int\:\frac{2x+5}{3x(x+3)^{2}}dx
(\partial)/(\partial y)(xy+8/x+8/y)	\frac{\partial\:}{\partial\:y}(xy+\frac{8}{x}+\frac{8}{y})
derivative of sqrt(7-2x)	\frac{d}{dx}(\sqrt{7-2x})
limit as x approaches 0 of xcot(7/11 x)	\lim\:_{x\to\:0}(x\cot(\frac{7}{11}x))
integral from 1 to e of x^2ln(x)	\int\:_{1}^{e}x^{2}\ln(x)dx
(dy)/(dx)=(sqrt(xy^2))	\frac{dy}{dx}=(\sqrt{xy^{2}})
limit as x approaches 0 of (3x)/(tan(x))	\lim\:_{x\to\:0}(\frac{3x}{\tan(x)})
y^'-2xy=2x	y^{\prime\:}-2xy=2x
limit as x approaches 1 of arctan(x)	\lim\:_{x\to\:1}(\arctan(x))
(\partial)/(\partial x)(xsin(xy))	\frac{\partial\:}{\partial\:x}(x\sin(xy))
integral of 5^x	\int\:5^{x}dx
y^'-4/x y= 1/(x^3)y^4	y^{\prime\:}-\frac{4}{x}y=\frac{1}{x^{3}}y^{4}
area arctan(x), pi/4 x,[0,2pi]	area\:\arctan(x),\frac{π}{4}x,[0,2π]
derivative of-30sin(x)	\frac{d}{dx}(-30\sin(x))

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