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Popular Calculus Problems

integral of 3ysqrt(7-3y^2)	\int\:3y\sqrt{7-3y^{2}}dy
integral from 0 to 1 of (y^2+y^4)	\int\:_{0}^{1}(y^{2}+y^{4})dy
derivative of x^2sqrt(3x+1)	\frac{d}{dx}(x^{2}\sqrt{3x+1})
integral of x/(sqrt(y^2+x^2))	\int\:\frac{x}{\sqrt{y^{2}+x^{2}}}dx
limit as x approaches 1 of (x^3-1)/(x-6)	\lim\:_{x\to\:1}(\frac{x^{3}-1}{x-6})
derivative of x^e	derivative\:x^{e}
integral of (2^x)/x	\int\:\frac{2^{x}}{x}dx
integral of (x^2)/((x^3-3)^2)	\int\:\frac{x^{2}}{(x^{3}-3)^{2}}dx
integral of-36sin(6t-pi/2)	\int\:-36\sin(6t-\frac{π}{2})dt
integral from 0 to 1 of 1/(sqrt(1+x))	\int\:_{0}^{1}\frac{1}{\sqrt{1+x}}dx
taylor 2sqrt(9+x^2)	taylor\:2\sqrt{9+x^{2}}
integral from 0 to 2pi of sin(x)	\int\:_{0}^{2π}\sin(x)dx
integral of 3sin(3x)+2cos(4x)	\int\:3\sin(3x)+2\cos(4x)dx
y^{'''}+2y^{''}-y^'-2y=sin(3t)	y^{\prime\:\prime\:\prime\:}+2y^{\prime\:\prime\:}-y^{\prime\:}-2y=\sin(3t)
derivative of (3x)/(sqrt(x))	derivative\:\frac{3x}{\sqrt{x}}
integral of-x^3-8x+5	\int\:-x^{3}-8x+5dx
limit as x approaches 0 of 1/(x+x^5)	\lim\:_{x\to\:0}(\frac{1}{x+x^{5}})
area 2x^2-x^3,y=0	area\:2x^{2}-x^{3},y=0
integral of-3/2 x^2	\int\:-\frac{3}{2}x^{2}dx
integral of (tan(x/(18)))^5	\int\:(\tan(\frac{x}{18}))^{5}dx
derivative of (4x/((1-x^2)^2))	\frac{d}{dx}(\frac{4x}{(1-x^{2})^{2}})
tangent of f(x)=x^2+3x+2,\at x=1	tangent\:f(x)=x^{2}+3x+2,\at\:x=1
laplacetransform e^{-2t}cos(2t)	laplacetransform\:e^{-2t}\cos(2t)
derivative of f(x)=7x^3	derivative\:f(x)=7x^{3}
(\partial)/(\partial x)(xe^{(x^2+y^2)})	\frac{\partial\:}{\partial\:x}(xe^{(x^{2}+y^{2})})
integral of sin^2(6x)cos^2(6x)	\int\:\sin^{2}(6x)\cos^{2}(6x)dx
area x^2,12-x	area\:x^{2},12-x
derivative of (x^3-y^3/(x-y))	\frac{d}{dx}(\frac{x^{3}-y^{3}}{x-y})
limit as x approaches 0 of+(x^x)	\lim\:_{x\to\:0}(+(x^{x}))
y^'=7ty^2	y^{\prime\:}=7ty^{2}
derivative of (ln(x))/(x^5)	derivative\:\frac{\ln(x)}{x^{5}}
limit as θ approaches 0 of (sin(7θ))/θ	\lim\:_{θ\to\:0}(\frac{\sin(7θ)}{θ})
derivative of x^2-5x+9	derivative\:x^{2}-5x+9
derivative of y=arccos(4x^4)	derivative\:y=\arccos(4x^{4})
(\partial)/(\partial x)(x/(x^2-2x+1))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}-2x+1})
derivative of ln(sqrt((x+1/(x-1))))	\frac{d}{dx}(\ln(\sqrt{\frac{x+1}{x-1}}))
slope ofintercept (-2,5.5),(0,5.5)	slopeintercept\:(-2,5.5),(0,5.5)
integral of (5x^2+x-34)/((x+1)^2(x-4))	\int\:\frac{5x^{2}+x-34}{(x+1)^{2}(x-4)}dx
derivative of x/2	derivative\:\frac{x}{2}
derivative of (2x+7/(2x))	\frac{d}{dx}(\frac{2x+7}{2x})
-(-x^3+y^3)dx+xy^2dy=0	-(-x^{3}+y^{3})dx+xy^{2}dy=0
integral of 1/(3x^2+4x-7)	\int\:\frac{1}{3x^{2}+4x-7}dx
derivative of x(x^5+9^3)	\frac{d}{dx}(x(x^{5}+9)^{3})
tangent of y=x^4-5x^3+3x^2-4x,(-1,13)	tangent\:y=x^{4}-5x^{3}+3x^{2}-4x,(-1,13)
(dy}{dx}=\frac{xy+x)/y	\frac{dy}{dx}=\frac{xy+x}{y}
limit as x approaches 1000 of x^{2/3}	\lim\:_{x\to\:1000}(x^{\frac{2}{3}})
derivative of 1/3 x^3-5x-4/x	\frac{d}{dx}(\frac{1}{3}x^{3}-5x-\frac{4}{x})
integral of x*ln^5(x)	\int\:x\cdot\:\ln^{5}(x)dx
y^{''}-4y^'+4y=e^x+xe^{2x}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=e^{x}+xe^{2x}
f(x)=cot(x^2)	f(x)=\cot(x^{2})
integral from-1 to 0 of x^3-x^2-2x	\int\:_{-1}^{0}x^{3}-x^{2}-2xdx
integral of x^4cos(2x)	\int\:x^{4}\cos(2x)dx
area 9-x^2,y=0	area\:9-x^{2},y=0
derivative of xsin(6x)	\frac{d}{dx}(x\sin(6x))
integral of 16y^3+9y^2-6y+3	\int\:16y^{3}+9y^{2}-6y+3dy
derivative of f(x)=\sqrt[x^4]{7-9x}	derivative\:f(x)=\sqrt[x^{4}]{7-9x}
integral from 0 to 1 of 4^{4x}	\int\:_{0}^{1}4^{4x}dx
integral of (cos(x))/(sin^2(x)-64)	\int\:\frac{\cos(x)}{\sin^{2}(x)-64}dx
integral of cos(2pi)	\int\:\cos(2π)dx
derivative of (cos(6x)/(e^x))	\frac{d}{dx}(\frac{\cos(6x)}{e^{x}})
derivative of y=arctan(x)	derivative\:y=\arctan(x)
x^2y^'=2x^2+xy+2y^2	x^{2}y^{\prime\:}=2x^{2}+xy+2y^{2}
integral of ((5-4x^2))/((3+2x))	\int\:\frac{(5-4x^{2})}{(3+2x)}dx
(\partial)/(\partial x)(xy+x+y)	\frac{\partial\:}{\partial\:x}(xy+x+y)
(y^{-1})^'	(y^{-1})^{\prime\:}
limit as x approaches-1 of (x+1)/(x^3+1)	\lim\:_{x\to\:-1}(\frac{x+1}{x^{3}+1})
y^'=-y+1/(sqrt(y))	y^{\prime\:}=-y+\frac{1}{\sqrt{y}}
derivative of sqrt(2-x)	derivative\:\sqrt{2-x}
derivative of e^{ln(x^2+1})	\frac{d}{dx}(e^{\ln(x^{2}+1)})
tangent of y=x^3-12x,(1,-11)	tangent\:y=x^{3}-12x,(1,-11)
derivative of-x+9/x+1	derivative\:-x+\frac{9}{x}+1
(\partial)/(\partial x)(x-8y+3xy)	\frac{\partial\:}{\partial\:x}(x-8y+3xy)
tangent of y=9x^2-x^3,(2,28)	tangent\:y=9x^{2}-x^{3},(2,28)
integral of ((cos(3x)))/(1+sin(3x))	\int\:\frac{(\cos(3x))}{1+\sin(3x)}dx
integral from 0 to 1 of 2pix(12-12x)	\int\:_{0}^{1}2πx(12-12x)dx
derivative of e^4	derivative\:e^{4}
y^{''}-9/t y^'+(34)/(t^2)y=0	y^{\prime\:\prime\:}-\frac{9}{t}y^{\prime\:}+\frac{34}{t^{2}}y=0
(\partial)/(\partial x)(1/(2sqrt(1+x+y)))	\frac{\partial\:}{\partial\:x}(\frac{1}{2\sqrt{1+x+y}})
(dy)/(dx)=(3x+xy^2)/(y+x^2y)	\frac{dy}{dx}=\frac{3x+xy^{2}}{y+x^{2}y}
integral of (e^{-x})/(1-e^{-2x)}	\int\:\frac{e^{-x}}{1-e^{-2x}}dx
(\partial)/(\partial x)(x^2-y^2+x+1)	\frac{\partial\:}{\partial\:x}(x^{2}-y^{2}+x+1)
derivative of (2x^2+4x+6)/(sqrt(x))	derivative\:\frac{2x^{2}+4x+6}{\sqrt{x}}
derivative of x^2+2x-1	\frac{d}{dx}(x^{2}+2x-1)
-4(dy)/(dx)+12x^2=0	-4\frac{dy}{dx}+12x^{2}=0
derivative of y=2x-3	derivative\:y=2x-3
area y=x+6,y=x^3,x=0	area\:y=x+6,y=x^{3},x=0
derivative of a^{-x}	\frac{d}{dx}(a^{-x})
d/(dt)(sqrt(3t+1))	\frac{d}{dt}(\sqrt{3t+1})
integral of-tln(t)	\int\:-t\ln(t)dt
tangent of x^2,\at x=0	tangent\:x^{2},\at\:x=0
(\partial)/(\partial y)(x^3yz^2)	\frac{\partial\:}{\partial\:y}(x^{3}yz^{2})
integral of [ 4/(16x^2+1)]	\int\:[\frac{4}{16x^{2}+1}]dx
tangent of f(x)=x^2-5x+5,(6,11)	tangent\:f(x)=x^{2}-5x+5,(6,11)
(\partial)/(\partial s)(s+t)	\frac{\partial\:}{\partial\:s}(s+t)
derivative of (x-3^{2/3})	\frac{d}{dx}((x-3)^{\frac{2}{3}})
integral of (2x)/(4-x^4)	\int\:\frac{2x}{4-x^{4}}dx
derivative of ln(sqrt(x^3))	\frac{d}{dx}(\ln(\sqrt{x^{3}}))
derivative of (1/2 x^5)	\frac{d}{dx}((\frac{1}{2}x)^{5})
limit as x approaches infinity of (x)^{(ln(2))/(1+ln(x))}	\lim\:_{x\to\:\infty\:}((x)^{\frac{\ln(2)}{1+\ln(x)}})
derivative of f(x)=(100)/((1+5x)^3)	derivative\:f(x)=\frac{100}{(1+5x)^{3}}

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