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Popular Calculus Problems

limit as x approaches-2 of (x^2-1)/(x-1)	\lim\:_{x\to\:-2}(\frac{x^{2}-1}{x-1})
integral of sin(x)(cos(x))^4	\int\:\sin(x)(\cos(x))^{4}dx
integral of (3x^2)/7	\int\:\frac{3x^{2}}{7}dx
y^'=3x^2	y^{\prime\:}=3x^{2}
(\partial)/(\partial x)(-7x^2-5y^2+xy)	\frac{\partial\:}{\partial\:x}(-7x^{2}-5y^{2}+xy)
inverse oflaplace ((4s^3))/((s+5)^9)	inverselaplace\:\frac{(4s^{3})}{(s+5)^{9}}
limit as x approaches 0 of ln(1-3x)	\lim\:_{x\to\:0}(\ln(1-3x))
integral of (e^{-x}-e^3)*(e^x+e^{-5})	\int\:(e^{-x}-e^{3})\cdot\:(e^{x}+e^{-5})dx
y^'+y*tan(x)= 1/(cos(x))	y^{\prime\:}+y\cdot\:\tan(x)=\frac{1}{\cos(x)}
taylor ln(1+12x)	taylor\:\ln(1+12x)
derivative of sqrt(x+16)	derivative\:\sqrt{x+16}
(\partial)/(\partial x)(10xyz)	\frac{\partial\:}{\partial\:x}(10xyz)
derivative of 27e^{3x}	\frac{d}{dx}(27e^{3x})
integral of (4x^3+1)ln(x)	\int\:(4x^{3}+1)\ln(x)dx
integral of x*sec^2(2x)	\int\:x\cdot\:\sec^{2}(2x)dx
x^2y^{''}+3xy^'=0	x^{2}y^{\prime\:\prime\:}+3xy^{\prime\:}=0
t*(dy)/(dt)+34y= 1/t	t\cdot\:\frac{dy}{dt}+34y=\frac{1}{t}
v+tv^'=((4+v))/((4v-1))	v+tv^{\prime\:}=\frac{(4+v)}{(4v-1)}
y^'=7x-y	y^{\prime\:}=7x-y
derivative of f(x)=3x^5(x^3-2x)	derivative\:f(x)=3x^{5}(x^{3}-2x)
integral of 3/(2sqrt(9-x^2))	\int\:\frac{3}{2\sqrt{9-x^{2}}}dx
integral of e^{3x}+1	\int\:e^{3x}+1dx
integral of 12x+24x^2	\int\:12x+24x^{2}dx
y^'-y=e^xy^2	y^{\prime\:}-y=e^{x}y^{2}
derivative of (x-43/(sqrt(x)-\sqrt{43)})	\frac{d}{dx}(\frac{x-43}{\sqrt{x}-\sqrt{43}})
integral of 6sin^4(xco)s^2x	\int\:6\sin^{4}(xco)s^{2}xdx
limit as x approaches 0+of d^2y	\lim\:_{x\to\:0+}(d^{2}y)
x^{''}+4x^'+8x=e^{-2t},x(0)=1,x^'(0)=-2	x^{\prime\:\prime\:}+4x^{\prime\:}+8x=e^{-2t},x(0)=1,x^{\prime\:}(0)=-2
derivative of cos(2x-1)	\frac{d}{dx}(\cos(2x)-1)
(dy)/(dx)-1/x y=0	\frac{dy}{dx}-\frac{1}{x}y=0
integral from-2 to 3 of (36)/(x^4)	\int\:_{-2}^{3}\frac{36}{x^{4}}dx
integral of 2ln(2x+1)	\int\:2\ln(2x+1)dx
derivative of \sqrt[3]{x}(2+x)	derivative\:\sqrt[3]{x}(2+x)
7(x^2+y^2)dx+2xydy=0	7(x^{2}+y^{2})dx+2xydy=0
integral of e^{-4x}cos(3x)	\int\:e^{-4x}\cos(3x)dx
derivative of-ln(x+x^2)	\frac{d}{dx}(-\ln(x)+x^{2})
integral from-6 to 8 of (x/2+8)	\int\:_{-6}^{8}(\frac{x}{2}+8)dx
integral of (3t^2)/2	\int\:\frac{3t^{2}}{2}dt
integral of sqrt(x)(ln(x))^2	\int\:\sqrt{x}(\ln(x))^{2}dx
derivative of 5ln(2x+6)	\frac{d}{dx}(5\ln(2x+6))
derivative of f(x)=(2x+6x^2)/((1+6x)^2)	derivative\:f(x)=\frac{2x+6x^{2}}{(1+6x)^{2}}
integral of (x+9)/(x^2+8x+20)	\int\:\frac{x+9}{x^{2}+8x+20}dx
limit as x approaches 9-of \sqrt[4]{9-x}	\lim\:_{x\to\:9-}(\sqrt[4]{9-x})
derivative of (2x+5^{1/2})	\frac{d}{dx}((2x+5)^{\frac{1}{2}})
d/(dt)(6cos(2t))	\frac{d}{dt}(6\cos(2t))
area y=x^3,y=x^2-9x,[-1,1]	area\:y=x^{3},y=x^{2}-9x,[-1,1]
integral of (3e^{5x}-7/x+4/(1+x^2))	\int\:(3e^{5x}-\frac{7}{x}+\frac{4}{1+x^{2}})dx
derivative of tan(x^2-1)	\frac{d}{dx}(\tan(x^{2}-1))
integral of 2xyz^3	\int\:2xyz^{3}dy
(dy)/(dx)=15-3y	\frac{dy}{dx}=15-3y
limit as x approaches 0 of (sin^6(x))/x	\lim\:_{x\to\:0}(\frac{\sin^{6}(x)}{x})
(\partial)/(\partial y)(x^2sin^2(y))	\frac{\partial\:}{\partial\:y}(x^{2}\sin^{2}(y))
derivative of 1^{1/3}	\frac{d}{dx}(1^{\frac{1}{3}})
x^2y^{''}+3xy^'+y= 1/x	x^{2}y^{\prime\:\prime\:}+3xy^{\prime\:}+y=\frac{1}{x}
derivative of (e^x(cos(x)))	\frac{d}{dx}((e^{x})(\cos(x)))
slope of (6.1)(1.1)	slope\:(6.1)(1.1)
(2x+y+1)((dy)/(dx))=1	(2x+y+1)(\frac{dy}{dx})=1
derivative of f(x)=(32)/(-4)	derivative\:f(x)=\frac{32}{-4}
integral from 3 to 4 of 3xcos(x^2)	\int\:_{3}^{4}3x\cos(x^{2})dx
integral of (3x+1)^3	\int\:(3x+1)^{3}dx
derivative of-3x^2	derivative\:-3x^{2}
d/(d{x)}(2{x}^2-4{x}{y}+3{y}^2+6{z}^2)	\frac{d}{d{x}}(2{x}^{2}-4{x}{y}+3{y}^{2}+6{z}^{2})
integral of (sqrt(x-3))/(x+3)	\int\:\frac{\sqrt{x-3}}{x+3}dx
derivative of 1/2 x^4-4x^2+4	\frac{d}{dx}(\frac{1}{2}x^{4}-4x^{2}+4)
derivative of y=6x	derivative\:y=6x
(\partial)/(\partial z)(xz-7yz+4)	\frac{\partial\:}{\partial\:z}(xz-7yz+4)
integral of e^{-st}cos(2t)	\int\:e^{-st}\cos(2t)dt
derivative of sqrt(x^2+3)	derivative\:\sqrt{x^{2}+3}
derivative of 2x^3sqrt(25-x^2)	derivative\:2x^{3}\sqrt{25-x^{2}}
limit as x approaches 0+of 1	\lim\:_{x\to\:0+}(1)
limit as x approaches 1 of (e^x)/(x-1)	\lim\:_{x\to\:1}(\frac{e^{x}}{x-1})
integral of 15arctan(sqrt(x))	\int\:15\arctan(\sqrt{x})dx
derivative of-x^2+4x	\frac{d}{dx}(-x^{2}+4x)
derivative of y=sqrt(x)(x-10)	derivative\:y=\sqrt{x}(x-10)
derivative of x/((x^2+y^2^2))	\frac{d}{dx}(\frac{x}{(x^{2}+y^{2})^{2}})
d/(dt)(2/(t^2+2))	\frac{d}{dt}(\frac{2}{t^{2}+2})
integral of 1/(-u^2-a+b)	\int\:\frac{1}{-u^{2}-a+b}du
d/(dt)(tan(e^{6t})+e^{tan(6t)})	\frac{d}{dt}(\tan(e^{6t})+e^{\tan(6t)})
(\partial)/(\partial x)(cos(xy)+e^{yz}+ln(zx))	\frac{\partial\:}{\partial\:x}(\cos(xy)+e^{yz}+\ln(zx))
tangent of f^9	tangent\:f^{9}
(dy)/(dx)=((2x+1))/(3y)	\frac{dy}{dx}=\frac{(2x+1)}{3y}
(dy)/(dx)=2y-4x	\frac{dy}{dx}=2y-4x
derivative of f(x)=x^2(6x+1)^3	derivative\:f(x)=x^{2}(6x+1)^{3}
integral of 3/(x^{-1)+1}	\int\:\frac{3}{x^{-1}+1}dx
derivative of sqrt(6+5x)	derivative\:\sqrt{6+5x}
area \|x\|,x^2-2	area\:\left\|x\right\|,x^{2}-2
derivative of sqrt(1-9x^2)arccos(3x)	derivative\:\sqrt{1-9x^{2}}\arccos(3x)
sum from n=2 to infinity of n	\sum\:_{n=2}^{\infty\:}n
derivative of f(t)=e^{3tsin(2t)}	derivative\:f(t)=e^{3t\sin(2t)}
derivative of (ln\|x\|^e+x/(11))	\frac{d}{dx}((\ln\left\|x\right\|)^{e}+\frac{x}{11})
25y^{''}-10y^'+y=0	25y^{\prime\:\prime\:}-10y^{\prime\:}+y=0
derivative of log_{3}(2x+5)	derivative\:\log_{3}(2x+5)
integral of (sec^2(t))/(1+tan(t))	\int\:\frac{\sec^{2}(t)}{1+\tan(t)}dt
integral of ((2y^{1/2})/(y^3))0x	\int\:(\frac{2y^{\frac{1}{2}}}{y^{3}})d^{0}x
derivative of (x^2+1/(x^2-4))	\frac{d}{dx}(\frac{x^{2}+1}{x^{2}-4})
(1+ln(x)+y/x)dx+(-1+ln(x))dy=0	(1+\ln(x)+\frac{y}{x})dx+(-1+\ln(x))dy=0
derivative of y=e^{3x}+10e^{2x}	derivative\:y=e^{3x}+10e^{2x}
limit as x approaches 0 of (2e^x-2)/(3x)	\lim\:_{x\to\:0}(\frac{2e^{x}-2}{3x})
derivative of te^{(-t)/2}	derivative\:te^{\frac{-t}{2}}
integral of 1/(x(x^2-81)^{3/2)}	\int\:\frac{1}{x(x^{2}-81)^{\frac{3}{2}}}dx

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