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Popular Calculus Problems

limit as x approaches-2 of (x^2)/(x^2-4)	\lim\:_{x\to\:-2}(\frac{x^{2}}{x^{2}-4})
integral of 1/(x^2+y^2)	\int\:\frac{1}{x^{2}+y^{2}}dx
integral of sin^4(8x)	\int\:\sin^{4}(8x)dx
derivative of nx^{n-1}	\frac{d}{dx}(nx^{n-1})
integral of-xe^{-4x}	\int\:-xe^{-4x}dx
derivative of f(x)=x^3-12x^2+48x	derivative\:f(x)=x^{3}-12x^{2}+48x
y^{''}+2y^'-8y=xe^{-x}+e^{-x}	y^{\prime\:\prime\:}+2y^{\prime\:}-8y=xe^{-x}+e^{-x}
(\partial)/(\partial x)(-u(x,y)cos(kx)sin(ky))	\frac{\partial\:}{\partial\:x}(-u(x,y)\cos(kx)\sin(ky))
derivative of 1/2 sec^2(x)	\frac{d}{dx}(\frac{1}{2}\sec^{2}(x))
derivative of x^{2/3}-a^{2/3}	\frac{d}{dx}(x^{\frac{2}{3}}-a^{\frac{2}{3}})
integral from 0 to 1 of x^3sqrt(1-x^4)	\int\:_{0}^{1}x^{3}\sqrt{1-x^{4}}dx
derivative of y(X)=(2X+5)/(sqrt(X))	derivative\:y(X)=\frac{2X+5}{\sqrt{X}}
(\partial)/(\partial x)(8ysqrt(x))	\frac{\partial\:}{\partial\:x}(8y\sqrt{x})
limit as h approaches 0 of ((2+h)-2)/h	\lim\:_{h\to\:0}(\frac{(2+h)-2}{h})
derivative of cos(2x+1)	derivative\:\cos(2x+1)
derivative of y=(1+2x)/(3-4x)	derivative\:y=\frac{1+2x}{3-4x}
limit as x approaches 0+of (e^x)/(1-e^x)	\lim\:_{x\to\:0+}(\frac{e^{x}}{1-e^{x}})
integral of cot(2x)	\int\:\cot(2x)dx
integral of (10)/(sqrt(2x+3))	\int\:\frac{10}{\sqrt{2x+3}}dx
(\partial)/(\partial x)(x^4+y^4-4xy+1)	\frac{\partial\:}{\partial\:x}(x^{4}+y^{4}-4xy+1)
(\partial)/(\partial x)(ln(3x^2+y^2+4))	\frac{\partial\:}{\partial\:x}(\ln(3x^{2}+y^{2}+4))
derivative of sec(x(x-tan(x)))	\frac{d}{dx}(\sec(x)(x-\tan(x)))
y^{''}+4y^'+4y=e^{-2x}	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=e^{-2x}
area x=6y^2,x=4+2y^2	area\:x=6y^{2},x=4+2y^{2}
tangent of f(x)=sqrt(x)(x^6-1),\at x=1	tangent\:f(x)=\sqrt{x}(x^{6}-1),\at\:x=1
integral of e^x*cos(3x)	\int\:e^{x}\cdot\:\cos(3x)dx
integral of (6x^2-15x+22)/((x+3)(x^2+2)^2)	\int\:\frac{6x^{2}-15x+22}{(x+3)(x^{2}+2)^{2}}dx
tangent of y= 1/(sqrt(x)),(4, 1/2)	tangent\:y=\frac{1}{\sqrt{x}},(4,\frac{1}{2})
y^{''}-3y^'+2y=e^{3t}	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=e^{3t}
(\partial)/(\partial x)(x^{sin(x)})	\frac{\partial\:}{\partial\:x}(x^{\sin(x)})
6*((dy)/(dx))=y^2,y(0)=4	6\cdot\:(\frac{dy}{dx})=y^{2},y(0)=4
tangent of y=x^3-2x+2,(3,23)	tangent\:y=x^{3}-2x+2,(3,23)
(dy)/(dx)=((3y^2))/(sqrt(x))	\frac{dy}{dx}=\frac{(3y^{2})}{\sqrt{x}}
y^'=((x^2y-y))/(y+1)	y^{\prime\:}=\frac{(x^{2}y-y)}{y+1}
derivative of 6	derivative\:6
(\partial)/(\partial x)(4x^4y^8+9x^6y^7)	\frac{\partial\:}{\partial\:x}(4x^{4}y^{8}+9x^{6}y^{7})
derivative of 2^x(x^2+1)	\frac{d}{dx}(2^{x}(x^{2}+1))
(2x-1)dx+(3y+5)dy=0	(2x-1)dx+(3y+5)dy=0
integral of (1+4x)^{3/5}	\int\:(1+4x)^{\frac{3}{5}}dx
(\partial)/(\partial x)(xsin(z))	\frac{\partial\:}{\partial\:x}(x\sin(z))
x^2y^'+2xy=e^{3x}	x^{2}y^{\prime\:}+2xy=e^{3x}
integral from 1 to 3 of (x^2+4)/x	\int\:_{1}^{3}\frac{x^{2}+4}{x}dx
integral of 20x^{19}	\int\:20x^{19}dx
integral from 0 to 1 of xsqrt(ax^2+b)	\int\:_{0}^{1}x\sqrt{ax^{2}+b}dx
derivative of sin^2(θ)	derivative\:\sin^{2}(θ)
y^'=(6t^2)/y	y^{\prime\:}=\frac{6t^{2}}{y}
integral from-1 to 1 of x^2sqrt(5-3x)	\int\:_{-1}^{1}x^{2}\sqrt{5-3x}dx
inverse oflaplace 3/(s^2+2s+5)	inverselaplace\:\frac{3}{s^{2}+2s+5}
derivative of 2x^4+3x-3	\frac{d}{dx}(2x^{4}+3x-3)
integral from-infinity to-1 of e^{-6t}	\int\:_{-\infty\:}^{-1}e^{-6t}dt
area 4sin(x),4cos(2x),-pi/2 , pi/6	area\:4\sin(x),4\cos(2x),-\frac{π}{2},\frac{π}{6}
derivative of (x-1(x+1)^2)	\frac{d}{dx}((x-1)(x+1)^{2})
limit as x approaches 0 of x^{ln(x)}	\lim\:_{x\to\:0}(x^{\ln(x)})
derivative of e^{8x}	derivative\:e^{8x}
limit as x approaches 0 of (cot(7x))/(csc(7x))	\lim\:_{x\to\:0}(\frac{\cot(7x)}{\csc(7x)})
dr=b(cos(θ)dr+rsin(θ)dθ)	dr=b(\cos(θ)dr+r\sin(θ)dθ)
derivative of (4t)/(t^2+25)	derivative\:\frac{4t}{t^{2}+25}
derivative of 2sin(2pix)	derivative\:2\sin(2πx)
derivative of sec(1/x)	derivative\:\sec(\frac{1}{x})
(\partial)/(\partial x)(ln(x+4y))	\frac{\partial\:}{\partial\:x}(\ln(x+4y))
integral of sin(7x)sin(9x)	\int\:\sin(7x)\sin(9x)dx
y^'+(1-2x)/(x^2)y=1	y^{\prime\:}+\frac{1-2x}{x^{2}}y=1
(\partial)/(\partial y)(2xy^4-1)	\frac{\partial\:}{\partial\:y}(2xy^{4}-1)
derivative of (5x^2+11x)^{4/3}	derivative\:(5x^{2}+11x)^{\frac{4}{3}}
integral of e^{-x(y+1)}	\int\:e^{-x(y+1)}dx
integral from 0 to 50 of 9.8(500-10y)	\int\:_{0}^{50}9.8(500-10y)dy
(\partial)/(\partial t)(2t)	\frac{\partial\:}{\partial\:t}(2t)
tangent of f(x)= 6/(4x+1),\at x=-1	tangent\:f(x)=\frac{6}{4x+1},\at\:x=-1
derivative of 3x^5-3x^4+x^3	derivative\:3x^{5}-3x^{4}+x^{3}
derivative of y=((x^3))/(3^x)	derivative\:y=\frac{(x^{3})}{3^{x}}
area 5x-x^2,y=0	area\:5x-x^{2},y=0
laplacetransform t^2-2t+2	laplacetransform\:t^{2}-2t+2
derivative of t^{22}ln\|t\|	derivative\:t^{22}\ln\left\|t\right\|
derivative of e^{2x}+xe^{2x}	\frac{d}{dx}(e^{2x}+xe^{2x})
taylor sqrt(3-x),0	taylor\:\sqrt{3-x},0
(2sqrt(x))^'	(2\sqrt{x})^{\prime\:}
derivative of x^2-25	\frac{d}{dx}(x^{2}-25)
tangent of f(x)=x^2+3x,\at x=0	tangent\:f(x)=x^{2}+3x,\at\:x=0
(\partial)/(\partial x)(sqrt(x)ln(t))	\frac{\partial\:}{\partial\:x}(\sqrt{x}\ln(t))
5y^'-15x^2=0	5y^{\prime\:}-15x^{2}=0
limit as n approaches 10 of [1+(1/n)]^n	\lim\:_{n\to\:10}([1+(\frac{1}{n})]^{n})
sum from n=0 to infinity of (i/3)^n	\sum\:_{n=0}^{\infty\:}(\frac{i}{3})^{n}
derivative of 2(1-x^{-3})	\frac{d}{dx}(2(1-x)^{-3})
limit as x approaches 0 of (5^x-4^x)/x	\lim\:_{x\to\:0}(\frac{5^{x}-4^{x}}{x})
derivative of (2x+3)/(3x+2)	derivative\:\frac{2x+3}{3x+2}
integral from 0 to 1 of z/((z^2+1)^3)	\int\:_{0}^{1}\frac{z}{(z^{2}+1)^{3}}dz
limit as x approaches 0+of ln(x^3)	\lim\:_{x\to\:0+}(\ln(x^{3}))
(1+t^2)y^'+4ty=t	(1+t^{2})y^{\prime\:}+4ty=t
limit as x approaches-4 of 1/((x+4)^4)	\lim\:_{x\to\:-4}(\frac{1}{(x+4)^{4}})
derivative of 10x+4y	\frac{d}{dx}(10x+4y)
derivative of 8tan(2x)	derivative\:8\tan(2x)
derivative of x^2-64	\frac{d}{dx}(x^{2}-64)
limit as x approaches 28 of (x^2)/4-7/x	\lim\:_{x\to\:28}(\frac{x^{2}}{4}-\frac{7}{x})
integral from-27 to 8 of 1/(\sqrt[3]{x)}	\int\:_{-27}^{8}\frac{1}{\sqrt[3]{x}}dx
2(dy)/(dx)-4xy=8x	2\frac{dy}{dx}-4xy=8x
limit as x approaches 2 of (x+5)(x-3)	\lim\:_{x\to\:2}((x+5)(x-3))
integral of t\sqrt[3]{t+10}	\int\:t\sqrt[3]{t+10}dt
derivative of x-x^2y-y+xy^2	\frac{d}{dx}(x-x^{2}y-y+xy^{2})
integral of sqrt(1+x^3)	\int\:\sqrt{1+x^{3}}dx
laplacetransform e^-cos(t)	laplacetransform\:e^{-}\cos(t)

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