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Popular Calculus Problems

limit as x approaches 0 of (x^3)/(x^6)	\lim\:_{x\to\:0}(\frac{x^{3}}{x^{6}})
(\partial)/(\partial y)(x^2+2y^2-x)	\frac{\partial\:}{\partial\:y}(x^{2}+2y^{2}-x)
integral of (2x-3)/(sqrt(4x-x^2))	\int\:\frac{2x-3}{\sqrt{4x-x^{2}}}dx
laplacetransform 8	laplacetransform\:8
integral of e^{tan(4x)}sec^2(4x)	\int\:e^{\tan(4x)}\sec^{2}(4x)dx
maclaurin 1/(1-x)	maclaurin\:\frac{1}{1-x}
integral from e to e^2 of 1/(xln(x))	\int\:_{e}^{e^{2}}\frac{1}{x\ln(x)}dx
parity f(x)=(e^x)/(sin(2x))	parity\:f(x)=\frac{e^{x}}{\sin(2x)}
derivative of (40/(1+79e^{-x)})	\frac{d}{dx}(\frac{40}{1+79e^{-x}})
derivative of x/(sqrt(x-7))	\frac{d}{dx}(\frac{x}{\sqrt{x-7}})
integral of (2x-1)/(4x^2-1)	\int\:\frac{2x-1}{4x^{2}-1}dx
integral from 0 to 4 of pi(4y^2-(y^4)/4)	\int\:_{0}^{4}π(4y^{2}-\frac{y^{4}}{4})dy
derivative of-4t(6t^4-1)^7	derivative\:-4t(6t^{4}-1)^{7}
integral from 0 to 1 of x^2(1+2x^3)^5	\int\:_{0}^{1}x^{2}(1+2x^{3})^{5}dx
derivative of y=(4x^2+6x+4)/(sqrt(x))	derivative\:y=\frac{4x^{2}+6x+4}{\sqrt{x}}
(\partial)/(\partial y)(5xy^2)	\frac{\partial\:}{\partial\:y}(5xy^{2})
integral of 4x^4sin(2x)	\int\:4x^{4}\sin(2x)dx
derivative of (x^5/(10)+1/(6x^3))	\frac{d}{dx}(\frac{x^{5}}{10}+\frac{1}{6x^{3}})
integral from 0 to (3pi)/2 of cos^3(9x)	\int\:_{0}^{\frac{3π}{2}}\cos^{3}(9x)dx
integral of 2/(3x+4)	\int\:\frac{2}{3x+4}dx
integral of (35)/(1-cos(5x))	\int\:\frac{35}{1-\cos(5x)}dx
xsin(x)e^{-y}dx-ydy=0	x\sin(x)e^{-y}dx-ydy=0
derivative of x^5+x+1	\frac{d}{dx}(x^{5}+x+1)
derivative of (((0.06x^2+17x+340))/x)	\frac{d}{dx}(\frac{((0.06x^{2})+17x+340)}{x})
derivative of (sin(x)/x)	\frac{d}{dx}(\frac{\sin(x)}{x})
integral of 11z^3e^z	\int\:11z^{3}e^{z}dz
laplacetransform 2e^{t/2}	laplacetransform\:2e^{\frac{t}{2}}
integral from 0 to 1 of ysqrt(1-y^2)	\int\:_{0}^{1}y\sqrt{1-y^{2}}dy
derivative of y=arctan(1)-x^1+x	derivative\:y=\arctan(1)-x^{1}+x
integral from 2 to t of 1/((5x^5))	\int\:_{2}^{t}\frac{1}{(5x^{5})}dx
integral of (tan^3(ln(x)))/(6x)	\int\:\frac{\tan^{3}(\ln(x))}{6x}dx
integral of 1/(P-P^2)	\int\:\frac{1}{P-P^{2}}dP
limit as x approaches 0 of 2/x	\lim\:_{x\to\:0}(\frac{2}{x})
limit as x approaches 0 of xsin((8pi)/x)	\lim\:_{x\to\:0}(x\sin(\frac{8π}{x}))
derivative of sqrt(x)cos(x^3)	\frac{d}{dx}(\sqrt{x}\cos(x^{3}))
limit as x approaches 0+of (1/x)^x	\lim\:_{x\to\:0+}((\frac{1}{x})^{x})
derivative of sin(arccos(t))	derivative\:\sin(\arccos(t))
integral of 1/(1-49x^2)	\int\:\frac{1}{1-49x^{2}}dx
integral of 2/(x-3)	\int\:\frac{2}{x-3}dx
integral of x/(x+4)	\int\:\frac{x}{x+4}dx
derivative of (x^2-3(x^3-2x))	\frac{d}{dx}((x^{2}-3)(x^{3}-2x))
tangent of f(x)=(2x)/(x^2-7),(3,3)	tangent\:f(x)=\frac{2x}{x^{2}-7},(3,3)
derivative of-11e^xsin(2x-2e^xcos(2x))	\frac{d}{dx}(-11e^{x}\sin(2x)-2e^{x}\cos(2x))
tangent of y=x^2+8,(4,24)	tangent\:y=x^{2}+8,(4,24)
(x^2+1)y^'+9x(y-1)=0	(x^{2}+1)y^{\prime\:}+9x(y-1)=0
integral of 1/(csc(x)-1)	\int\:\frac{1}{\csc(x)-1}dx
limit as x approaches 0 of (5e^x-5)/x	\lim\:_{x\to\:0}(\frac{5e^{x}-5}{x})
integral of (cos(x))^4	\int\:(\cos(x))^{4}dx
integral from 0 to 1 of 3/(sqrt(4-x^2))	\int\:_{0}^{1}\frac{3}{\sqrt{4-x^{2}}}dx
derivative of f(x)=(x-3)/(x+4)	derivative\:f(x)=\frac{x-3}{x+4}
inverse oflaplace s/(s^2+3)	inverselaplace\:\frac{s}{s^{2}+3}
integral of 5tan^5(x)	\int\:5\tan^{5}(x)dx
laplacetransform t^2-4t+4	laplacetransform\:t^{2}-4t+4
xdx+ydy=xy(xdy-ydx)	xdx+ydy=xy(xdy-ydx)
derivative of-6x^{1/4}	\frac{d}{dx}(-6x^{\frac{1}{4}})
integral of 1/(x(x-1))	\int\:\frac{1}{x(x-1)}dx
integral from 6 to 7 of x^{pi-1}	\int\:_{6}^{7}x^{π-1}dx
limit as x approaches 1 of 1/(2x-1)	\lim\:_{x\to\:1}(\frac{1}{2x-1})
derivative of (2x^2-1^6)	\frac{d}{dx}((2x^{2}-1)^{6})
integral of e^{-2x} 1 (y)-2e^{-2x}y	\int\:e^{-2x}\frac{d}{1}(y)-2e^{-2x}ydx
(\partial)/(\partial x)(x/(sqrt(x^2+y^3)))	\frac{\partial\:}{\partial\:x}(\frac{x}{\sqrt{x^{2}+y^{3}}})
y^'+7=e^{7x+y-5},y(0)=5	y^{\prime\:}+7=e^{7x+y-5},y(0)=5
sum from n=0 to infinity of (n+2)/(n+1)	\sum\:_{n=0}^{\infty\:}\frac{n+2}{n+1}
area 1/4 x^2-1,0,2,8	area\:\frac{1}{4}x^{2}-1,0,2,8
integral from 0 to 2 of 1/((x-1)^2)	\int\:_{0}^{2}\frac{1}{(x-1)^{2}}dx
y=2sin(x)	y=2\sin(x)
(\partial)/(\partial x)(sqrt(x)+sqrt(y))	\frac{\partial\:}{\partial\:x}(\sqrt{x}+\sqrt{y})
tangent of f(x)=-x^3+4x-2,\at x=-2	tangent\:f(x)=-x^{3}+4x-2,\at\:x=-2
taylor 1/(1-4x)	taylor\:\frac{1}{1-4x}
integral of sin^5(xco)s^3x	\int\:\sin^{5}(xco)s^{3}xdx
tangent of f(x)=-3x^{3/2},\at x=4	tangent\:f(x)=-3x^{\frac{3}{2}},\at\:x=4
(\partial)/(\partial x)(xye^x)	\frac{\partial\:}{\partial\:x}(xye^{x})
y^{''}+8y^'+20y=0,y(0)=3,y^'(0)=-11	y^{\prime\:\prime\:}+8y^{\prime\:}+20y=0,y(0)=3,y^{\prime\:}(0)=-11
derivative of-2x^3+12x^2-18x	\frac{d}{dx}(-2x^{3}+12x^{2}-18x)
(\partial)/(\partial x)(((4x+y))/(x-3y))	\frac{\partial\:}{\partial\:x}(\frac{(4x+y)}{x-3y})
derivative of sqrt(arctan(x/2))	\frac{d}{dx}(\sqrt{\arctan(\frac{x}{2})})
integral of (8x^7+2x)/(x^8+x^2)	\int\:\frac{8x^{7}+2x}{x^{8}+x^{2}}dx
(\partial)/(\partial y)((2x)/(y^2))	\frac{\partial\:}{\partial\:y}(\frac{2x}{y^{2}})
y^'=8(y^2+1)	y^{\prime\:}=8(y^{2}+1)
integral of xtan(x^2-1)	\int\:x\tan(x^{2}-1)dx
integral of xsqrt(x^2+8)	\int\:x\sqrt{x^{2}+8}dx
limit as x approaches 0 of ln(x-1)	\lim\:_{x\to\:0}(\ln(x-1))
x(dy}{dx}+2y=\frac{sin(x))/x	x\frac{dy}{dx}+2y=\frac{\sin(x)}{x}
integral of cos(x/7)	\int\:\cos(\frac{x}{7})dx
2y^{''}+3y^'-2y=2x-3	2y^{\prime\:\prime\:}+3y^{\prime\:}-2y=2x-3
y^{''}-8y^'+16y=t^{-4}e^{4t}	y^{\prime\:\prime\:}-8y^{\prime\:}+16y=t^{-4}e^{4t}
integral from 1 to 2 of 5x^2ln(x)	\int\:_{1}^{2}5x^{2}\ln(x)dx
f(x)=6x^{1/2}	f(x)=6x^{\frac{1}{2}}
derivative of y=12x^2-7x-2x^{-2}	derivative\:y=12x^{2}-7x-2x^{-2}
integral of (cos^3(x))/(sqrt(sin(x)))	\int\:\frac{\cos^{3}(x)}{\sqrt{\sin(x)}}dx
integral of cos(5x-1)	\int\:\cos(5x-1)dx
derivative of f(x)=6x^5(x^3-6x)	derivative\:f(x)=6x^{5}(x^{3}-6x)
integral from 0 to 1 of 9/(sqrt(x)(x+1))	\int\:_{0}^{1}\frac{9}{\sqrt{x}(x+1)}dx
derivative of 3xarctan(x^2+e^{sin(x)})	\frac{d}{dx}(3x\arctan(x^{2})+e^{\sin(x)})
integral of 3xsqrt(x+5)	\int\:3x\sqrt{x+5}dx
derivative of xln(x^3)	\frac{d}{dx}(x\ln(x^{3}))
integral from 1 to infinity of xe^{-14x}	\int\:_{1}^{\infty\:}xe^{-14x}dx
13(t+1)(dy)/(dt)-9y=36t	13(t+1)\frac{dy}{dt}-9y=36t
integral of xcos(10x)	\int\:x\cos(10x)dx
derivative of arcsec(1/x)	\frac{d}{dx}(\arcsec(\frac{1}{x}))

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