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Popular Calculus Problems

derivative of y=arcsin(x+1)	derivative\:y=\arcsin(x+1)
integral of 2/3 x^{3/2}-9sin(x)	\int\:\frac{2}{3}x^{\frac{3}{2}}-9\sin(x)dx
(\partial)/(\partial x)(7xsin(y-z))	\frac{\partial\:}{\partial\:x}(7x\sin(y-z))
limit as x approaches 8 of (sqrt(7+\sqrt[3]{x)}-3)/(x-8)	\lim\:_{x\to\:8}(\frac{\sqrt{7+\sqrt[3]{x}}-3}{x-8})
integral of 3x^2-2y^2	\int\:3x^{2}-2y^{2}dx
integral of x/(1-2x)	\int\:\frac{x}{1-2x}dx
limit as x approaches 1 of sqrt(3+f(x))	\lim\:_{x\to\:1}(\sqrt{3+f(x)})
integral of t^2e^{-4t}	\int\:t^{2}e^{-4t}dt
derivative of (4x/(7x-2))	\frac{d}{dx}(\frac{4x}{7x-2})
inverse oflaplace 1/((2s+1)s)	inverselaplace\:\frac{1}{(2s+1)s}
integral of x^2ln(9x)	\int\:x^{2}\ln(9x)dx
derivative of (tan^2(x)/(tan(x^2)))	\frac{d}{dx}(\frac{\tan^{2}(x)}{\tan(x^{2})})
sqrt(x)(dy)/(dx)=e^{7y+sqrt(x)}	\sqrt{x}\frac{dy}{dx}=e^{7y+\sqrt{x}}
sum from n=1 to infinity of 5(-1/6)^{5n}	\sum\:_{n=1}^{\infty\:}5(-\frac{1}{6})^{5n}
derivative of f(x)=(2x^2-x-1)/(2x+2)	derivative\:f(x)=\frac{2x^{2}-x-1}{2x+2}
limit as x approaches 0+of x^{20x}	\lim\:_{x\to\:0+}(x^{20x})
derivative of 7x^4cot(x)	\frac{d}{dx}(7x^{4}\cot(x))
xydx-(1+x^2)dy=0	xydx-(1+x^{2})dy=0
x''	x\prime\:\prime\:
(dy)/(dx)+3y=40	\frac{dy}{dx}+3y=40
derivative of sqrt(x)(2x+4)	\frac{d}{dx}(\sqrt{x}(2x+4))
limit as x approaches 7 of (x+6)/(x+1)	\lim\:_{x\to\:7}(\frac{x+6}{x+1})
tangent of (x^3+2x)^3,\at x=4	tangent\:(x^{3}+2x)^{3},\at\:x=4
integral from 0 to 2 of x^6	\int\:_{0}^{2}x^{6}dx
integral of xcos(4pi)x^2	\int\:x\cos(4π)x^{2}dx
derivative of (x^2+x+2/(2x))	\frac{d}{dx}(\frac{x^{2}+x+2}{2x})
area y=2x^2,y=2x+6	area\:y=2x^{2},y=2x+6
derivative of ln(x)	derivative\:\ln(x)
derivative of (e^x-e^{-x}/5)	\frac{d}{dx}(\frac{e^{x}-e^{-x}}{5})
(xdy)/(dx)=y+sqrt(x^2-y^2)	\frac{xdy}{dx}=y+\sqrt{x^{2}-y^{2}}
integral from-1/4 to 1/4 of 1/(1-x^2)	\int\:_{-\frac{1}{4}}^{\frac{1}{4}}\frac{1}{1-x^{2}}dx
laplacetransform-9t^2	laplacetransform\:-9t^{2}
integral of (3x)/(1+x^2)	\int\:\frac{3x}{1+x^{2}}dx
integral of (-2sqrt(x))	\int\:(-2\sqrt{x})dx
(\partial)/(\partial x)(x+y^3)	\frac{\partial\:}{\partial\:x}(x+y^{3})
(\partial)/(\partial x)(2yx-3y+y^2)	\frac{\partial\:}{\partial\:x}(2yx-3y+y^{2})
ye^{xy}dx+xe^{xy}dy=0	ye^{xy}dx+xe^{xy}dy=0
derivative of a/(bx^2)	\frac{d}{dx}(\frac{a}{bx^{2}})
derivative of 2x	derivative\:2x
inverse oflaplace ((s-10))/((s^2-2s-3))	inverselaplace\:\frac{(s-10)}{(s^{2}-2s-3)}
implicit (dy)/(dx),x^6-5xy^3=9xy	implicit\:\frac{dy}{dx},x^{6}-5xy^{3}=9xy
limit as x approaches 0 of arctan(1/x)	\lim\:_{x\to\:0}(\arctan(\frac{1}{x}))
integral of (x^2+2)/(x^3(x+1)^3)	\int\:\frac{x^{2}+2}{x^{3}(x+1)^{3}}dx
area 1/((sqrt(1-7x))),-6<x<0	area\:\frac{1}{(\sqrt{1-7x})},-6<x<0
(\partial)/(\partial x)(4x^{-x^2-y^2-z^2})	\frac{\partial\:}{\partial\:x}(4x^{-x^{2}-y^{2}-z^{2}})
integral of 7.9t-16.6	\int\:7.9t-16.6dt
derivative of 1/((1-2x^{3/2)})	\frac{d}{dx}(\frac{1}{(1-2x)^{\frac{3}{2}}})
(\partial)/(\partial x)(x^{2/3}+y^{2/3})	\frac{\partial\:}{\partial\:x}(x^{\frac{2}{3}}+y^{\frac{2}{3}})
integral of 1/(sqrt(64+x^2))	\int\:\frac{1}{\sqrt{64+x^{2}}}dx
f(x)=xcos(x)	f(x)=x\cos(x)
derivative of ln(x+2x)	\frac{d}{dx}(\ln(x)+2x)
taylor 1/(1+x^2),0	taylor\:\frac{1}{1+x^{2}},0
integral from 0 to 1 of (1-x^7)^2	\int\:_{0}^{1}(1-x^{7})^{2}dx
derivative of x^3-2x^2-4x+6	derivative\:x^{3}-2x^{2}-4x+6
y^{''}-2y^'=x+2e^x,y(0)=18,y^'(0)= 31/4	y^{\prime\:\prime\:}-2y^{\prime\:}=x+2e^{x},y(0)=18,y^{\prime\:}(0)=\frac{31}{4}
derivative of 2cos(x+3sin(x))	\frac{d}{dx}(2\cos(x)+3\sin(x))
inverse oflaplace (s+3)/(s^2+2s+2)	inverselaplace\:\frac{s+3}{s^{2}+2s+2}
tangent of 5x^2+8x-8	tangent\:5x^{2}+8x-8
d/(du)(sqrt(u))	\frac{d}{du}(\sqrt{u})
derivative of (6x-1(5x-2)^{-1})	\frac{d}{dx}((6x-1)(5x-2)^{-1})
derivative of 2(x-1^2)	\frac{d}{dx}(2(x-1)^{2})
y^{''}+4y^'+5y=-10x+3e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=-10x+3e^{-x}
limit as x approaches 3 of sqrt(x-2)	\lim\:_{x\to\:3}(\sqrt{x-2})
integral of (sec^2(x))/x	\int\:\frac{\sec^{2}(x)}{x}dx
derivative of f(x)=(x+5)/(x-5)	derivative\:f(x)=\frac{x+5}{x-5}
limit as x approaches-2 of x^2-4/(x+2)	\lim\:_{x\to\:-2}(x^{2}-\frac{4}{x+2})
area y=cos(x),y=0.5,0<= x<= pi	area\:y=\cos(x),y=0.5,0\le\:x\le\:π
1296y^{''}+1368y^'+361y=0	1296y^{\prime\:\prime\:}+1368y^{\prime\:}+361y=0
x(dy)/(dx)=y+(x^2-2)^2	x\frac{dy}{dx}=y+(x^{2}-2)^{2}
integral of sin^2(pix)cos^5(pix)	\int\:\sin^{2}(πx)\cos^{5}(πx)dx
derivative of \sqrt[3]{6+2x+x^3}	derivative\:\sqrt[3]{6+2x+x^{3}}
derivative of csc^2(1-2x)	\frac{d}{dx}(\csc^{2}(1-2x))
limit as x approaches-1 of 3x^4-6x+1	\lim\:_{x\to\:-1}(3x^{4}-6x+1)
integral of 3x^2+2x	\int\:3x^{2}+2xdx
limit as x approaches 2 of x^3-5x	\lim\:_{x\to\:2}(x^{3}-5x)
limit as x approaches-6+of sqrt(x+6)	\lim\:_{x\to\:-6+}(\sqrt{x+6})
derivative of 3\sqrt[3]{x^2}-2x	\frac{d}{dx}(3\sqrt[3]{x^{2}}-2x)
integral of 1/(sqrt(cos(x)+cos^2(x)))	\int\:\frac{1}{\sqrt{\cos(x)+\cos^{2}(x)}}dx
(\partial)/(\partial z)(ln(1+xy)-z)	\frac{\partial\:}{\partial\:z}(\ln(1+xy)-z)
derivative of f(x)=sqrt(x+8)	derivative\:f(x)=\sqrt{x+8}
integral of tln(1+t)	\int\:t\ln(1+t)dt
integral from-8 to 0 of (y/8+sqrt(y+9))	\int\:_{-8}^{0}(\frac{y}{8}+\sqrt{y+9})dy
limit as x approaches infinity of x+9	\lim\:_{x\to\:\infty\:}(x+9)
integral of 1/(x^2+3x+3)	\int\:\frac{1}{x^{2}+3x+3}dx
y''(x)-3y'(x)+2y= 1/(1+e^{-x)}	y\prime\:\prime\:(x)-3y\prime\:(x)+2y=\frac{1}{1+e^{-x}}
limit as x approaches 0 of-arcsin(x)	\lim\:_{x\to\:0}(-\arcsin(x))
derivative of 5e^x+2/(\sqrt[3]{x})	\frac{d}{dx}(5e^{x}+\frac{2}{\sqrt[3]{x}})
integral from 0 to 1 of 9cos((pit)/2)	\int\:_{0}^{1}9\cos(\frac{πt}{2})dt
integral of 1/(sqrt(x^2+36))	\int\:\frac{1}{\sqrt{x^{2}+36}}dx
derivative of ln(3)	derivative\:\ln(3)
derivative of ln(1/(1-x))	\frac{d}{dx}(\ln(\frac{1}{1-x}))
area y=4x^2,y=x^2+6	area\:y=4x^{2},y=x^{2}+6
limit as x approaches 7 of x+2	\lim\:_{x\to\:7}(x+2)
integral of xe^xln(x-1)	\int\:xe^{x}\ln(x-1)dx
integral of (sin^5(ln(x)))/x	\int\:\frac{\sin^{5}(\ln(x))}{x}dx
limit as x approaches 0 of (sqrt(5+x)-sqrt(5))/(2x)	\lim\:_{x\to\:0}(\frac{\sqrt{5+x}-\sqrt{5}}{2x})
derivative of f(t)=e^{7tsin(2t)}	derivative\:f(t)=e^{7t\sin(2t)}
tangent of f(x)=x(27x^{-2}+2),\at x=-3	tangent\:f(x)=x(27x^{-2}+2),\at\:x=-3
(\partial)/(\partial x)((x-1)/(x+1))	\frac{\partial\:}{\partial\:x}(\frac{x-1}{x+1})
integral from 0 to infinity of 1/(e^x-1)	\int\:_{0}^{\infty\:}\frac{1}{e^{x}-1}dx

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