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Popular Calculus Problems

(d^2)/(dx^2)((ln(x))^2)	\frac{d^{2}}{dx^{2}}((\ln(x))^{2})
derivative of y=((x+1))/(x^3+x-2)	derivative\:y=\frac{(x+1)}{x^{3}+x-2}
derivative of e^{4xy}	\frac{d}{dx}(e^{4xy})
integral of cos^3(5x)sin^{-2}(5x)	\int\:\cos^{3}(5x)\sin^{-2}(5x)dx
integral of 2e^{-3x}	\int\:2e^{-3x}dx
limit as x approaches 0 of cos^{1/x}(x)	\lim\:_{x\to\:0}(\cos^{\frac{1}{x}}(x))
sin^2(y)dx+cos^2(x)dy=0	\sin^{2}(y)dx+\cos^{2}(x)dy=0
limit as x approaches-5 of 2x+3	\lim\:_{x\to\:-5}(2x+3)
inverse oflaplace (1+e^{-pis})/(s^2+1)	inverselaplace\:\frac{1+e^{-πs}}{s^{2}+1}
tangent of f(x)=2sec(x),\at x= pi/3	tangent\:f(x)=2\sec(x),\at\:x=\frac{π}{3}
inverse oflaplace e^{3s}	inverselaplace\:e^{3s}
integral from-pi/2 to pi/2 of 1	\int\:_{-\frac{π}{2}}^{\frac{π}{2}}1dx
limit as x approaches infinity of pi/x	\lim\:_{x\to\:\infty\:}(\frac{π}{x})
(\partial)/(\partial x)(4cos^3(kx-wt)-3cos(kx-wt))	\frac{\partial\:}{\partial\:x}(4\cos^{3}(kx-wt)-3\cos(kx-wt))
tangent of sin(5x)+cos(2x)	tangent\:\sin(5x)+\cos(2x)
integral of e^{15x}	\int\:e^{15x}dx
integral of tan^3(5x)sec^5(5x)	\int\:\tan^{3}(5x)\sec^{5}(5x)dx
derivative of (6x^2+8^6)	\frac{d}{dx}((6x^{2}+8)^{6})
integral from 0 to 3 of-x^2+3x	\int\:_{0}^{3}-x^{2}+3xdx
(\partial)/(\partial x)(x^2ye^y)	\frac{\partial\:}{\partial\:x}(x^{2}ye^{y})
y^{''}-y^'+484y=22sin(22t)	y^{\prime\:\prime\:}-y^{\prime\:}+484y=22\sin(22t)
integral of tan(x)cos(x)	\int\:\tan(x)\cos(x)dx
derivative of (8-x^3)	\frac{d}{dx}((8-x)^{3})
integral of 1/(2+x^2)	\int\:\frac{1}{2+x^{2}}dx
limit as x approaches 4 of (x^2-16)/(2x^2+7x-4)	\lim\:_{x\to\:4}(\frac{x^{2}-16}{2x^{2}+7x-4})
sin(2x)dx+cos(5y)dy=0	\sin(2x)dx+\cos(5y)dy=0
derivative of ln(x^2+y^2-1)	\frac{d}{dx}(\ln(x^{2})+y^{2}-1)
derivative of (((3x+1)/(x^2))^3)	\frac{d}{dx}((\frac{(3x+1)}{x^{2}})^{3})
limit as x approaches+0 of x(x-[x])	\lim\:_{x\to\:+0}(x(x-[x]))
(\partial)/(\partial x)(-2y^3sin(2x))	\frac{\partial\:}{\partial\:x}(-2y^{3}\sin(2x))
dx-x+ydy=0	dx-x+ydy=0
integral of e^{17x}	\int\:e^{17x}dx
(\partial)/(\partial y)(3xyz+xy^2-xz^3)	\frac{\partial\:}{\partial\:y}(3xyz+xy^{2}-xz^{3})
42y^{''}+29y^'-5y=0	42y^{\prime\:\prime\:}+29y^{\prime\:}-5y=0
sum from n=1 to infinity of n/((3+n))	\sum\:_{n=1}^{\infty\:}\frac{n}{(3+n)}
derivative of ln(3x^3+x+6)	\frac{d}{dx}(\ln(3x^{3}+x+6))
derivative of (1+x^2/(1+x))	\frac{d}{dx}(\frac{1+x^{2}}{1+x})
derivative of (16)/((1-x)^3)	derivative\:\frac{16}{(1-x)^{3}}
integral of ((sqrt(9-x^2)))/(x^2)	\int\:\frac{(\sqrt{9-x^{2}})}{x^{2}}dx
integral of x/((x^2+8)^2)	\int\:\frac{x}{(x^{2}+8)^{2}}dx
derivative of f(x)=x^{-12}	derivative\:f(x)=x^{-12}
derivative of 4x^3+4x^2-8x	\frac{d}{dx}(4x^{3}+4x^{2}-8x)
derivative of ln(x+sqrt(x^2-11))	\frac{d}{dx}(\ln(x+\sqrt{x^{2}-11}))
derivative of f(x)=x+3	derivative\:f(x)=x+3
(dy)/(dx)=y(xy^6+4)	\frac{dy}{dx}=y(xy^{6}+4)
sum from n=1 to infinity of 1/((3n-1)^4)	\sum\:_{n=1}^{\infty\:}\frac{1}{(3n-1)^{4}}
y^'+5xy=0	y^{\prime\:}+5xy=0
limit as x approaches-1 of 2/(x^2-1)	\lim\:_{x\to\:-1}(\frac{2}{x^{2}-1})
tangent of x^3-7x	tangent\:x^{3}-7x
integral of sin(3xy)	\int\:\sin(3xy)dx
tangent of f(x)=x+sqrt(x)	tangent\:f(x)=x+\sqrt{x}
integral of (-3)/((x^2+3)^{3/2)}	\int\:\frac{-3}{(x^{2}+3)^{\frac{3}{2}}}dx
area y=-x^2-x,y=3x	area\:y=-x^{2}-x,y=3x
((dx)/(dy))=k(a-x)(a-x)	(\frac{dx}{dy})=k(a-x)(a-x)
derivative of 1/(12x)	derivative\:\frac{1}{12x}
derivative of 5x-x^{-1/3}-1	\frac{d}{dx}(5x-x^{-\frac{1}{3}}-1)
integral of x^2sec(x^3-1)	\int\:x^{2}\sec(x^{3}-1)dx
derivative of \sqrt[3]{(2-3x^2})	\frac{d}{dx}(\sqrt[3]{(2-3x)^{2}})
derivative of ((x-2)/((x+3)^2))	\frac{d}{dx}(\frac{(x-2)}{(x+3)^{2}})
integral of (12)/(x^2-9)	\int\:\frac{12}{x^{2}-9}dx
derivative of (1+csc(x^5)/(1-cot(x^5)))	\frac{d}{dx}(\frac{1+\csc(x^{5})}{1-\cot(x^{5})})
integral of (y^3)/3	\int\:\frac{y^{3}}{3}dy
(\partial)/(\partial x)(2yarctan(x/y))	\frac{\partial\:}{\partial\:x}(2y\arctan(\frac{x}{y}))
integral of sin(x-2)	\int\:\sin(x-2)dx
derivative of (18)/x	derivative\:\frac{18}{x}
integral of (x^3)/(sqrt(x^2+2))	\int\:\frac{x^{3}}{\sqrt{x^{2}+2}}dx
integral of e^{-(x^2+1)}	\int\:e^{-(x^{2}+1)}dx
y^{''}+4y=cos(4x),y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+4y=\cos(4x),y(0)=0,y^{\prime\:}(0)=0
(\partial)/(\partial x)(13(3^x))	\frac{\partial\:}{\partial\:x}(13(3^{x}))
derivative of x/(30)	\frac{d}{dx}(\frac{x}{30})
integral of (9x^2-3x+19)/((x^2+4)(x-3))	\int\:\frac{9x^{2}-3x+19}{(x^{2}+4)(x-3)}dx
integral from-pi to pi of xsin(x)	\int\:_{-π}^{π}x\sin(x)dx
area 3(x^3-x),0,-1,1	area\:3(x^{3}-x),0,-1,1
derivative of 5xln(3x)	\frac{d}{dx}(5x\ln(3x))
(\partial)/(\partial x)(xcos(y))	\frac{\partial\:}{\partial\:x}(x\cos(y))
integral of x^2cos(x^3+10)	\int\:x^{2}\cos(x^{3}+10)dx
taylor ln(1-x)	taylor\:\ln(1-x)
integral of (y^5)/(1-y^4)	\int\:\frac{y^{5}}{1-y^{4}}dy
(\partial)/(\partial t)(s/t)	\frac{\partial\:}{\partial\:t}(\frac{s}{t})
limit as x approaches 4 of 2x^4-x^2-8x	\lim\:_{x\to\:4}(2x^{4}-x^{2}-8x)
integral from 0 to 2 of x\sqrt[3]{4+x^2}	\int\:_{0}^{2}x\sqrt[3]{4+x^{2}}dx
(\partial)/(\partial x)(3/(3x+5y))	\frac{\partial\:}{\partial\:x}(\frac{3}{3x+5y})
area 6x^2ln(x),24ln(x)	area\:6x^{2}\ln(x),24\ln(x)
(dy)/(dx)= 1/2 x+2	\frac{dy}{dx}=\frac{1}{2}x+2
x^2y^{''}+3xy^'+2y=0,y(1)=0.2,y^'(1)=0.3	x^{2}y^{\prime\:\prime\:}+3xy^{\prime\:}+2y=0,y(1)=0.2,y^{\prime\:}(1)=0.3
derivative of cos(sqrt(sin(tan(pix))))	\frac{d}{dx}(\cos(\sqrt{\sin(\tan(π)x)}))
laplacetransform 3*sin(3t+2)	laplacetransform\:3\cdot\:\sin(3t+2)
integral of cos(X)	\int\:\cos(X)dX
derivative of x(7x+3^{1/3})	\frac{d}{dx}(x(7x+3)^{\frac{1}{3}})
derivative of 11^x	derivative\:11^{x}
derivative of y=(2x-3)(x+3)^3	derivative\:y=(2x-3)(x+3)^{3}
y^'=y(xy^3+2)	y^{\prime\:}=y(xy^{3}+2)
integral of e^{3x}e^x	\int\:e^{3x}e^{x}dx
derivative of-sin(x-1)	\frac{d}{dx}(-\sin(x)-1)
(\partial)/(\partial x)(xln(xy-5))	\frac{\partial\:}{\partial\:x}(x\ln(xy-5))
limit as x approaches 3 of x^2+4	\lim\:_{x\to\:3}(x^{2}+4)
integral from-1 to 1 of x(1.5x^2)	\int\:_{-1}^{1}x(1.5x^{2})dx
derivative of ln((x+1/(sqrt(x-1))))	\frac{d}{dx}(\ln(\frac{x+1}{\sqrt{x-1}}))
derivative of 4/((x^2+9^3))	\frac{d}{dx}(\frac{4}{(x^{2}+9)^{3}})
derivative of 2cos(2t)	derivative\:2\cos(2t)

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