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Popular Calculus Problems

derivative of \sqrt[3]{5x}+4x^{1/2}-3x	\frac{d}{dx}(\sqrt[3]{5x}+4x^{\frac{1}{2}}-3x)
derivative of 2xln(4x^2)	\frac{d}{dx}(2x\ln(4x^{2}))
integral of (60)/(2x+5)-5	\int\:\frac{60}{2x+5}-5dx
integral of cot(x)(-8sin(x)-10csc(x))	\int\:\cot(x)(-8\sin(x)-10\csc(x))dx
y^2+x^2y^'=0	y^{2}+x^{2}y^{\prime\:}=0
integral of x(x+2)^{-3/2}	\int\:x(x+2)^{-\frac{3}{2}}dx
integral of e^{cos(4x)}sin(4x)	\int\:e^{\cos(4x)}\sin(4x)dx
t^2y^{''}+6ty^'+6y=0	t^{2}y^{\prime\:\prime\:}+6ty^{\prime\:}+6y=0
2xy^2+4=2(3-x^2y)y^'	2xy^{2}+4=2(3-x^{2}y)y^{\prime\:}
integral of 1/4 cos(2x)	\int\:\frac{1}{4}\cos(2x)dx
(\partial)/(\partial y)(sqrt(1+x^2+y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{1+x^{2}+y^{2}})
integral of (3x^2+2)	\int\:(3x^{2}+2)dx
integral from 0 to 1 of 6x^2(3-5x^3)^3	\int\:_{0}^{1}6x^{2}(3-5x^{3})^{3}dx
integral of 1/(xInx)	\int\:\frac{1}{xInx}dx
derivative of 4/(sqrt(3x+9))	derivative\:\frac{4}{\sqrt{3x+9}}
integral of 1/(sinh^2(x)+cosh^2(x))	\int\:\frac{1}{\sinh^{2}(x)+\cosh^{2}(x)}dx
integral of ((ln(x))^{23})/x	\int\:\frac{(\ln(x))^{23}}{x}dx
(\partial)/(\partial x)(2*ln(x)+y)	\frac{\partial\:}{\partial\:x}(2\cdot\:\ln(x)+y)
derivative of 2x^2e^{-x}	\frac{d}{dx}(2x^{2}e^{-x})
limit as x approaches 0 of (x^2)/(x^2)	\lim\:_{x\to\:0}(\frac{x^{2}}{x^{2}})
(\partial)/(\partial y)(sqrt(x^2-y))	\frac{\partial\:}{\partial\:y}(\sqrt{x^{2}-y})
integral of e^{x^2+1}2x	\int\:e^{x^{2}+1}2xdx
(dy)/(dx)(1/(x^8))-15y=12	\frac{dy}{dx}(\frac{1}{x^{8}})-15y=12
integral of 4+6x+24x^2	\int\:4+6x+24x^{2}dx
taylor ln(1-2y)	taylor\:\ln(1-2y)
(\partial)/(\partial x)(2x+2xy)	\frac{\partial\:}{\partial\:x}(2x+2xy)
(x+2y)dx+(2x+y)dy=0	(x+2y)dx+(2x+y)dy=0
integral of 42sec^4(x)	\int\:42\sec^{4}(x)dx
area x^2,0,2	area\:x^{2},0,2
integral of x 1/(sqrt(1-x^2))	\int\:x\frac{1}{\sqrt{1-x^{2}}}dx
derivative of 10cos^3(x)	\frac{d}{dx}(10\cos^{3}(x))
derivative of f(x)=sin(x)+3/4 cot(x)	derivative\:f(x)=\sin(x)+\frac{3}{4}\cot(x)
derivative of (1+7/x ^5)	\frac{d}{dx}((1+\frac{7}{x})^{5})
limit as x approaches-3 of sqrt(5x^2+2x)	\lim\:_{x\to\:-3}(\sqrt{5x^{2}+2x})
integral of (1+x)/(1-\sqrt[3]{x)}	\int\:\frac{1+x}{1-\sqrt[3]{x}}dx
limit as x approaches 3 of (x-2)/(x-3)	\lim\:_{x\to\:3}(\frac{x-2}{x-3})
integral of 3/(4(4-3x)^7)	\int\:\frac{3}{4(4-3x)^{7}}dx
4y^{''}+9y=0	4y^{\prime\:\prime\:}+9y=0
derivative of f(x)=2x^2+5x	derivative\:f(x)=2x^{2}+5x
area-x^2+4x+1,x+1	area\:-x^{2}+4x+1,x+1
integral of ((y-3))/y	\int\:\frac{(y-3)}{y}dy
inverse oflaplace 1/(x^2)	inverselaplace\:\frac{1}{x^{2}}
derivative of (t+3)(2t-1)^2	derivative\:(t+3)(2t-1)^{2}
sum from n=0 to infinity of n*(4/5)^n	\sum\:_{n=0}^{\infty\:}n\cdot\:(\frac{4}{5})^{n}
(d^2)/(dx^2)((3+2x)e^{-5x})	\frac{d^{2}}{dx^{2}}((3+2x)e^{-5x})
tangent of f(x)=sqrt(x^2+1),\at x=1	tangent\:f(x)=\sqrt{x^{2}+1},\at\:x=1
limit as x approaches 2 of 3x^2-5x+1	\lim\:_{x\to\:2}(3x^{2}-5x+1)
integral from 0 to 1 of x^5	\int\:_{0}^{1}x^{5}dx
x^3y^{'''}-3x^2y^{''}+6xy^'-6y=0	x^{3}y^{\prime\:\prime\:\prime\:}-3x^{2}y^{\prime\:\prime\:}+6xy^{\prime\:}-6y=0
derivative of sqrt(15t^2+9)	derivative\:\sqrt{15t^{2}+9}
(\partial)/(\partial x)(7x^2e^y)	\frac{\partial\:}{\partial\:x}(7x^{2}e^{y})
integral of (4/(sqrt(x))+4sqrt(x))	\int\:(\frac{4}{\sqrt{x}}+4\sqrt{x})dx
(arctan(x^2))^'	(\arctan(x^{2}))^{\prime\:}
integral of x/((x^2-9)^2)	\int\:\frac{x}{(x^{2}-9)^{2}}dx
derivative of f(x)=(sqrt(5))/(x^6)	derivative\:f(x)=\frac{\sqrt{5}}{x^{6}}
integral of (x-1)^2+1	\int\:(x-1)^{2}+1dx
((1+x^2)dy)/(dx)-(1+y^2)=0	\frac{(1+x^{2})dy}{dx}-(1+y^{2})=0
integral from 0 to N of e^{-st}e^{-5t}	\int\:_{0}^{N}e^{-st}e^{-5t}dt
(ydy+xdx)/(2sqrt(1+xy))=0	\frac{ydy+xdx}{2\sqrt{1+xy}}=0
(d^2)/(dx^2)((x^2+5)^6)	\frac{d^{2}}{dx^{2}}((x^{2}+5)^{6})
(\partial)/(\partial x)(4y^2x^3)	\frac{\partial\:}{\partial\:x}(4y^{2}x^{3})
integral from 0 to 1 of (x+1)(x^2+2x)^5	\int\:_{0}^{1}(x+1)(x^{2}+2x)^{5}dx
integral of (-1800x)/(sqrt(25-x^2))	\int\:\frac{-1800x}{\sqrt{25-x^{2}}}dx
laplacetransform t^2cos(3t)	laplacetransform\:t^{2}\cos(3t)
limit as x approaches 13 of x^4-10x^2-20	\lim\:_{x\to\:13}(x^{4}-10x^{2}-20)
limit as x approaches infinity of xe^{(1/x)}	\lim\:_{x\to\:\infty\:}(xe^{(\frac{1}{x})})
inverse oflaplace (s^2+4)/((s^2-4)^2)	inverselaplace\:\frac{s^{2}+4}{(s^{2}-4)^{2}}
5x-8ysqrt(x^2+1)(dy)/(dx)=0	5x-8y\sqrt{x^{2}+1}\frac{dy}{dx}=0
simplify 2ln((3x^2)/2)	simplify\:2\ln(\frac{3x^{2}}{2})
derivative of (4x^2+9(8x+x^{1/2}))	\frac{d}{dx}((4x^{2}+9)(8x+x^{\frac{1}{2}}))
derivative of y=7x^{1/2}+x^{3/2}	derivative\:y=7x^{\frac{1}{2}}+x^{\frac{3}{2}}
integral of (5x)/(sqrt(3x^2+4))	\int\:\frac{5x}{\sqrt{3x^{2}+4}}dx
integral of x^2sqrt(8x+9)	\int\:x^{2}\sqrt{8x+9}dx
(\partial)/(\partial y)((y^3)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{y^{3}}{x^{2}+y^{2}})
sum from n=0 to infinity of (3n^9)/(n!)	\sum\:_{n=0}^{\infty\:}\frac{3n^{9}}{n!}
derivative of 3cos(x+3sin(x))	\frac{d}{dx}(3\cos(x)+3\sin(x))
integral of (x+3)^{1/2}	\int\:(x+3)^{\frac{1}{2}}dx
(dy)/(dx)7x^3+7y^3-5xy=0	\frac{dy}{dx}7x^{3}+7y^{3}-5xy=0
integral of 1/(x(5+9ln(x)))	\int\:\frac{1}{x(5+9\ln(x))}dx
derivative of (8x^2+9)(x^2-1/x)	derivative\:(8x^{2}+9)(x^{2}-\frac{1}{x})
tangent of 6x^2-4x+5	tangent\:6x^{2}-4x+5
integral of ((x^4-5x^2+3x-4))/x	\int\:\frac{(x^{4}-5x^{2}+3x-4)}{x}dx
integral from 1 to e of ((x^2-1)/x)	\int\:_{1}^{e}(\frac{x^{2}-1}{x})dx
derivative of ln((x+y/(x-y)))	\frac{d}{dx}(\ln(\frac{x+y}{x-y}))
derivative of ln(2x^4e^{3x}(x^2+x+1^5))	\frac{d}{dx}(\ln(2x^{4}e^{3x}(x^{2}+x+1)^{5}))
integral of (3-x)/(3-x^2)	\int\:\frac{3-x}{3-x^{2}}dx
integral from-2 to 5 of-2	\int\:_{-2}^{5}-2dx
integral of (x-2)/((x^2+x+2)(x^2+2))	\int\:\frac{x-2}{(x^{2}+x+2)(x^{2}+2)}dx
derivative of xln(x-x+1)	\frac{d}{dx}(x\ln(x)-x+1)
integral of ((1+15x))/x	\int\:\frac{(1+15x)}{x}dx
integral of (x+5)/(x+1)	\int\:\frac{x+5}{x+1}dx
inverse oflaplace-1/(s(s^2+1))	inverselaplace\:-\frac{1}{s(s^{2}+1)}
y^{''}+4y=8sin(2x)	y^{\prime\:\prime\:}+4y=8\sin(2x)
limit as x approaches 0.5 of (sin(x))/x	\lim\:_{x\to\:0.5}(\frac{\sin(x)}{x})
integral of cos^2((3pix)/L)	\int\:\cos^{2}(\frac{3πx}{L})dx
sum from n=0 to infinity of (-3/10)^n	\sum\:_{n=0}^{\infty\:}(-\frac{3}{10})^{n}
slope of (4,-3),(7,-2)	slope\:(4,-3),(7,-2)
derivative of x/(12)	\frac{d}{dx}(\frac{x}{12})
(\partial)/(\partial x)((xy+yz+xz)^2)	\frac{\partial\:}{\partial\:x}((xy+yz+xz)^{2})
integral from 0 to pi/(30) of tan(15x)	\int\:_{0}^{\frac{π}{30}}\tan(15x)dx

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