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Popular Calculus Problems

area sin(x),cos(x),-pi/(18), 9/4	area\:\sin(x),\cos(x),-\frac{π}{18},\frac{9}{4}
derivative of b+c(x-a^{2/3})	\frac{d}{dx}(b+c(x-a)^{\frac{2}{3}})
limit as x approaches-2 of (x^2-4)/(x-2)	\lim\:_{x\to\:-2}(\frac{x^{2}-4}{x-2})
derivative of x^5+5	\frac{d}{dx}(x^{5}+5)
area f(x)=x(x+2)(x-1),{-2,1}	area\:f(x)=x(x+2)(x-1),\left\{-2,1\right\}
integral of cos(nxpi)	\int\:\cos(nxπ)dx
derivative of f(x)=(x+6)/(x-6)	derivative\:f(x)=\frac{x+6}{x-6}
taylor (1-x)e^{x+(x^2)/2}	taylor\:(1-x)e^{x+\frac{x^{2}}{2}}
limit as x approaches 0+of-x^2ln(6x^3)	\lim\:_{x\to\:0+}(-x^{2}\ln(6x^{3}))
integral of 6/(5+6x)	\int\:\frac{6}{5+6x}dx
integral of e^x2	\int\:e^{x}2dx
(\partial)/(\partial x)(6e^{xy+5})	\frac{\partial\:}{\partial\:x}(6e^{xy+5})
taylor ln(((1+x))/(1-x))	taylor\:\ln(\frac{(1+x)}{1-x})
derivative of-(x-3^2(1-x)^2)	\frac{d}{dx}(-(x-3)^{2}(1-x)^{2})
(\partial)/(\partial x)((4x+4)(ln(8xy)))	\frac{\partial\:}{\partial\:x}((4x+4)(\ln(8xy)))
derivative of Ax^2e^{-2x}	\frac{d}{dx}(Ax^{2}e^{-2x})
integral of (sec^2(x)-5)	\int\:(\sec^{2}(x)-5)dx
tangent of f(x)=(1+5x)^9,\at x=0	tangent\:f(x)=(1+5x)^{9},\at\:x=0
limit as x approaches 0+of (Inx)/x	\lim\:_{x\to\:0+}(\frac{Inx}{x})
(dy)/(dx)=((xy+3x-y-3))/(xy-2x+4y-8)	\frac{dy}{dx}=\frac{(xy+3x-y-3)}{xy-2x+4y-8}
integral of (2x)/(x^2+x)	\int\:\frac{2x}{x^{2}+x}dx
inverse oflaplace s/(s+4)	inverselaplace\:\frac{s}{s+4}
(dy)/(dx)= 1/(x+y)	\frac{dy}{dx}=\frac{1}{x+y}
(\partial)/(\partial x)(5x^2y-5x+4y^3)	\frac{\partial\:}{\partial\:x}(5x^{2}y-5x+4y^{3})
integral of x^2(e^x)	\int\:x^{2}(e^{x})dx
limit as x approaches-2 of (2x+2)/(x-1)	\lim\:_{x\to\:-2}(\frac{2x+2}{x-1})
derivative of (6x)/(1-tan(x))	derivative\:\frac{6x}{1-\tan(x)}
integral of (sqrt(x-3))/(sqrt(x+1))	\int\:\frac{\sqrt{x-3}}{\sqrt{x+1}}dx
y^{''}-y^'-6y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}-y^{\prime\:}-6y=0,y(0)=1,y^{\prime\:}(0)=0
integral of 9/(x(x+3))	\int\:\frac{9}{x(x+3)}dx
integral of ln(y)	\int\:\ln(y)dy
integral of 3x^2-24x+36	\int\:3x^{2}-24x+36dx
d/(d{x)}(e^{{x}}cos({y}{z}))	\frac{d}{d{x}}(e^{{x}}\cos({y}{z}))
(dy)/(dx)=((x-y))/(x+2y),y(0)=1	\frac{dy}{dx}=\frac{(x-y)}{x+2y},y(0)=1
f^{''}(x)=x^{1/14}	f^{\prime\:\prime\:}(x)=x^{\frac{1}{14}}
integral from 1 to 2 of 3^{-θ}	\int\:_{1}^{2}3^{-θ}dθ
integral of 5x^4e^{6x^5}	\int\:5x^{4}e^{6x^{5}}dx
derivative of ln(cos(ln(7x)))	derivative\:\ln(\cos(\ln(7x)))
limit as x approaches 0 of sin(8x)	\lim\:_{x\to\:0}(\sin(8x))
(\partial)/(\partial x)(x^2e^{xy^2})	\frac{\partial\:}{\partial\:x}(x^{2}e^{xy^{2}})
integral of (2x^2)/(sqrt(9-x^2))	\int\:\frac{2x^{2}}{\sqrt{9-x^{2}}}dx
integral from 0 to 1 of 2pi(2-y)(7-7y^2)	\int\:_{0}^{1}2π(2-y)(7-7y^{2})dy
inverse oflaplace 3/(4s)	inverselaplace\:\frac{3}{4s}
derivative of sec^2(x^3)	\frac{d}{dx}(\sec^{2}(x^{3}))
limit as x approaches 2 of-x+7	\lim\:_{x\to\:2}(-x+7)
integral of (x^3)/(x^4+6)	\int\:\frac{x^{3}}{x^{4}+6}dx
tangent of f(x)=ln(x^7),(1,0)	tangent\:f(x)=\ln(x^{7}),(1,0)
(dy}{dx}=\frac{2x+5y)/x	\frac{dy}{dx}=\frac{2x+5y}{x}
simplify-2/3 sqrt(x^3)-sqrt(15x)-\sqrt[3]{x^5}	simplify\:-\frac{2}{3}\sqrt{x^{3}}-\sqrt{15x}-\sqrt[3]{x^{5}}
derivative of 6/((x+1^4))	\frac{d}{dx}(\frac{6}{(x+1)^{4}})
derivative of (x^2/(sqrt(x+1)))	\frac{d}{dx}(\frac{x^{2}}{\sqrt{x+1}})
integral of (x^2-1)/(x^{3/2)}	\int\:\frac{x^{2}-1}{x^{\frac{3}{2}}}dx
limit as x approaches-1 of (4x-5)/(3-x)	\lim\:_{x\to\:-1}(\frac{4x-5}{3-x})
tangent of f(x)=sqrt(x^2-x+19),\at x=3	tangent\:f(x)=\sqrt{x^{2}-x+19},\at\:x=3
integral of 1/((x-1)^{1/3)}	\int\:\frac{1}{(x-1)^{\frac{1}{3}}}dx
tangent of f(x)=(x-1)(x-3)^2,\at x=4	tangent\:f(x)=(x-1)(x-3)^{2},\at\:x=4
(1+2y)dx-(4-x)dy=0	(1+2y)dx-(4-x)dy=0
derivative of f(x)=sqrt(13x)	derivative\:f(x)=\sqrt{13x}
derivative of arcsin(7x+1)	\frac{d}{dx}(\arcsin(7x+1))
integral of (8x^3)	\int\:(8x^{3})dx
integral of 4xcos(2x)	\int\:4x\cos(2x)dx
limit as x approaches 2 of 2x+4	\lim\:_{x\to\:2}(2x+4)
(\partial)/(\partial x)(xdy)	\frac{\partial\:}{\partial\:x}(xdy)
derivative of-e^x+3sqrt(x)-3sin(x)	derivative\:-e^{x}+3\sqrt{x}-3\sin(x)
derivative of (sin(x^2+1)^{1/y})	\frac{d}{dx}((\sin(x^{2})+1)^{\frac{1}{y}})
(\partial)/(\partial x)(sin(pi(6x-3y)))	\frac{\partial\:}{\partial\:x}(\sin(π(6x-3y)))
(\partial)/(\partial x)(xy-5x^2y)	\frac{\partial\:}{\partial\:x}(xy-5x^{2}y)
(d^2)/(dx^2)f(x)=5x^3+12x^2+8x+22	\frac{d^{2}}{dx^{2}}f(x)=5x^{3}+12x^{2}+8x+22
(\partial)/(\partial x)(4(y-1)(x-4)^3)	\frac{\partial\:}{\partial\:x}(4(y-1)(x-4)^{3})
integral of ye^{0.2y}	\int\:ye^{0.2y}dy
integral from 0 to pi of 3tan(x/3)	\int\:_{0}^{π}3\tan(\frac{x}{3})dx
derivative of 1+sec^2(x)	\frac{d}{dx}(1+\sec^{2}(x))
limit as x approaches 2 of (x-9)/(x-9x)	\lim\:_{x\to\:2}(\frac{x-9}{x-9x})
integral from 4 to 7 of x^3ln(4x)	\int\:_{4}^{7}x^{3}\ln(4x)dx
derivative of e^{7/u}	derivative\:e^{\frac{7}{u}}
(dx)/(dt)=x-2	\frac{dx}{dt}=x-2
integral of csc(3/4)xcot(3/4)x	\int\:\csc(\frac{3}{4})x\cot(\frac{3}{4})xdx
(dx)/(dt)+(10x)/(20000-5t)=5	\frac{dx}{dt}+\frac{10x}{20000-5t}=5
sum from n=0 to infinity of (n^n)/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{n^{n}}{2^{n}}
integral of-tan(x)+1	\int\:-\tan(x)+1dx
integral of (1-x)ln(x)	\int\:(1-x)\ln(x)dx
integral of (sin(2x))/(1+sin^2(x))	\int\:\frac{\sin(2x)}{1+\sin^{2}(x)}dx
derivative of sqrt(2x)sin(x)	\frac{d}{dx}(\sqrt{2x}\sin(x))
(\partial)/(\partial y)(sin(x^3y^2))	\frac{\partial\:}{\partial\:y}(\sin(x^{3}y^{2}))
(\partial)/(\partial y)(3x^2y^4-4)	\frac{\partial\:}{\partial\:y}(3x^{2}y^{4}-4)
derivative of 2/(x^2+3)	derivative\:\frac{2}{x^{2}+3}
derivative of 2ax+b	derivative\:2ax+b
(dy}{dx}=\frac{2x)/y	\frac{dy}{dx}=\frac{2x}{y}
integral from-8 to 8 of x^{1/3}	\int\:_{-8}^{8}x^{\frac{1}{3}}dx
y^{''}-1/x y^'=3x	y^{\prime\:\prime\:}-\frac{1}{x}y^{\prime\:}=3x
integral from 1 to 4 of x^3	\int\:_{1}^{4}x^{3}dx
derivative of cos(x+2)	\frac{d}{dx}(\cos(x+2))
derivative of (x^2/(7+4x))	\frac{d}{dx}(\frac{x^{2}}{7+4x})
integral of 6/(9-x^2)	\int\:\frac{6}{9-x^{2}}dx
integral of (x^4)/(1-x^5)	\int\:\frac{x^{4}}{1-x^{5}}dx
integral of 1/(x-5)	\int\:\frac{1}{x-5}dx
integral of 1/(sqrt(400-x^2))	\int\:\frac{1}{\sqrt{400-x^{2}}}dx
t(x)v''+v'=0	t(x)v\prime\:\prime\:+v\prime\:=0
integral of 3/(xln(5x))	\int\:\frac{3}{x\ln(5x)}dx
y^{10}(dy)/(dx)=-9cos(pix)	y^{10}\frac{dy}{dx}=-9\cos(πx)

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