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Popular Calculus Problems

integral of (x/(sqrt(1-x^2)))	\int\:(\frac{x}{\sqrt{1-x^{2}}})dx
integral from-4 to 0 of \|x+2\|	\int\:_{-4}^{0}\left\|x+2\right\|dx
(\partial)/(\partial x)(4-x^2-2y^2)	\frac{\partial\:}{\partial\:x}(4-x^{2}-2y^{2})
derivative of Ax^2e^{3x}	\frac{d}{dx}(Ax^{2}e^{3x})
x(dy)/(dx)=3xe^x-y+6x^2	x\frac{dy}{dx}=3xe^{x}-y+6x^{2}
limit as x approaches 1 of x^{4/(1-x)}	\lim\:_{x\to\:1}(x^{\frac{4}{1-x}})
integral of sqrt(-x^2+25)	\int\:\sqrt{-x^{2}+25}dx
y^{''}+3y^'-40y=0	y^{\prime\:\prime\:}+3y^{\prime\:}-40y=0
integral of (-2)/(t+1)	\int\:\frac{-2}{t+1}dt
inverse oflaplace (1200)/(s^2(s+10)^2)	inverselaplace\:\frac{1200}{s^{2}(s+10)^{2}}
derivative of (2x^3-6)/(x^4)	derivative\:\frac{2x^{3}-6}{x^{4}}
derivative of (xcos(x-sin(x))/(x^2))	\frac{d}{dx}(\frac{x\cos(x)-\sin(x)}{x^{2}})
(\partial)/(\partial x)(30x^5y^4-20x^4y^3)	\frac{\partial\:}{\partial\:x}(30x^{5}y^{4}-20x^{4}y^{3})
limit as x approaches-2 of 1/(x^2)	\lim\:_{x\to\:-2}(\frac{1}{x^{2}})
tangent of x^2+y^2=169,(12,-5)	tangent\:x^{2}+y^{2}=169,(12,-5)
derivative of (4x-13ln((2x-7)(x-3)))	\frac{d}{dx}((4x-13)\ln((2x-7)(x-3)))
integral from-2 to 3 of (8z^3+3z-1)	\int\:_{-2}^{3}(8z^{3}+3z-1)dz
integral from 1 to infinity of ((e^{-sqrt(x)}))/(sqrt(x))	\int\:_{1}^{\infty\:}\frac{(e^{-\sqrt{x}})}{\sqrt{x}}dx
integral of sqrt(75-10x-x^2)	\int\:\sqrt{75-10x-x^{2}}dx
y^{''}-y^'-2y=-4t+8t^2	y^{\prime\:\prime\:}-y^{\prime\:}-2y=-4t+8t^{2}
area y=sqrt(x-2),y=x^2-4,x=5	area\:y=\sqrt{x-2},y=x^{2}-4,x=5
integral of ycos(z)	\int\:y\cos(z)dz
xy=(-1-x^2)y^'	xy=(-1-x^{2})y^{\prime\:}
integral of 2x^{-1/2}	\int\:2x^{-\frac{1}{2}}dx
derivative of 7(4x^2-7x+2)^{-6}	derivative\:7(4x^{2}-7x+2)^{-6}
limit as x approaches infinity of x^2+5	\lim\:_{x\to\:\infty\:}(x^{2}+5)
limit as x approaches 2-of (x-1)/(x-2)	\lim\:_{x\to\:2-}(\frac{x-1}{x-2})
limit as x approaches pi/2 of cos^{cos(x)}(x)	\lim\:_{x\to\:\frac{π}{2}}(\cos^{\cos(x)}(x))
derivative of te^{2t}	derivative\:te^{2t}
tangent of ((sqrt(x)+1))/((sqrt(x)+7))	tangent\:\frac{(\sqrt{x}+1)}{(\sqrt{x}+7)}
integral of 3/(xsqrt(4-9ln^2(x)))	\int\:\frac{3}{x\sqrt{4-9\ln^{2}(x)}}dx
derivative of (4x^{3/2})/x	derivative\:\frac{4x^{\frac{3}{2}}}{x}
y^{''}+4y^'+4y=-(18te-2t+8t+4)	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=-(18te-2t+8t+4)
derivative of f(x)=x^2-10x	derivative\:f(x)=x^{2}-10x
(\partial)/(\partial x)(5x^7cos(y^8))	\frac{\partial\:}{\partial\:x}(5x^{7}\cos(y^{8}))
limit as x approaches 0 of 1+sin(x)-e^x	\lim\:_{x\to\:0}(1+\sin(x)-e^{x})
integral of-x^2+x+2	\int\:-x^{2}+x+2dx
integral of (8x-5^x)	\int\:(8x-5^{x})dx
(dy)/(dx)=ky^2ln(x)	\frac{dy}{dx}=ky^{2}\ln(x)
limit as x approaches 0 of 1-2/(3x)	\lim\:_{x\to\:0}(1-\frac{2}{3x})
limit as x approaches pi of (cos(x)-1)/x	\lim\:_{x\to\:π}(\frac{\cos(x)-1}{x})
derivative of sqrt(x)(x-9^2)	\frac{d}{dx}(\sqrt{x}(x-9)^{2})
integral of (4x+sqrt(x))	\int\:(4x+\sqrt{x})dx
tangent of y=sqrt(x),\at x= 1/4	tangent\:y=\sqrt{x},\at\:x=\frac{1}{4}
integral of (ln^5(x^2))/x	\int\:\frac{\ln^{5}(x^{2})}{x}dx
derivative of-6x^2+6x	\frac{d}{dx}(-6x^{2}+6x)
integral of 2(3-e^{-t})	\int\:2(3-e^{-t})dt
inverse oflaplace 2/(s^2+4s+3)	inverselaplace\:\frac{2}{s^{2}+4s+3}
derivative of-x^2sin(x^2y)	\frac{d}{dx}(-x^{2}\sin(x^{2}y))
limit as x approaches 3 of x^3-3x^2-9x	\lim\:_{x\to\:3}(x^{3}-3x^{2}-9x)
(xdy)/(dx)-y=sqrt(x^2+y^2)	\frac{xdy}{dx}-y=\sqrt{x^{2}+y^{2}}
integral of (z^{-3})/3	\int\:\frac{z^{-3}}{3}dz
y^{''}+16y=2tan(4x)	y^{\prime\:\prime\:}+16y=2\tan(4x)
limit as x approaches-1 of 2x	\lim\:_{x\to\:-1}(2x)
integral from 0 to pi of cos(nx)	\int\:_{0}^{π}\cos(nx)dx
integral from 0 to e of ln(x^2)	\int\:_{0}^{e}\ln(x^{2})dx
integral from-1 to 1 of (\sqrt[3]{x}-2)	\int\:_{-1}^{1}(\sqrt[3]{x}-2)dx
tangent of y= 3/(sqrt(x))	tangent\:y=\frac{3}{\sqrt{x}}
integral of sin^2(x)cos^2(2x)	\int\:\sin^{2}(x)\cos^{2}(2x)dx
derivative of {f}(xsqrt(x))	\frac{d}{dx}({f}(x)\sqrt{x})
limit as x approaches-3+of (\|x+3\|)/(x+3)	\lim\:_{x\to\:-3+}(\frac{\left\|x+3\right\|}{x+3})
derivative of 30e^{-0.0000323x}	derivative\:30e^{-0.0000323x}
integral from-4 to 0 of sqrt(y+4)	\int\:_{-4}^{0}\sqrt{y+4}dy
integral of (10x+2)/((3x+1)(x-1))	\int\:\frac{10x+2}{(3x+1)(x-1)}dx
integral of x^2+8	\int\:x^{2}+8dx
derivative of y	derivative\:y
9y^{''}+6y^'+y=0	9y^{\prime\:\prime\:}+6y^{\prime\:}+y=0
(2y-x^2y)y^'=x(y+2)^2	(2y-x^{2}y)y^{\prime\:}=x(y+2)^{2}
derivative of y=(sin(2x)+3cos(x))/(x+1)	derivative\:y=\frac{\sin(2x)+3\cos(x)}{x+1}
integral of csch(x)	\int\:\csch(x)dx
derivative of \sqrt[3]{x}+(x^{1/3})/3	derivative\:\sqrt[3]{x}+\frac{x^{\frac{1}{3}}}{3}
derivative of F(X)=X-ln(1+X)	derivative\:F(X)=X-\ln(1+X)
integral of (66x^2)/(x^4-65x^2+784)	\int\:\frac{66x^{2}}{x^{4}-65x^{2}+784}dx
(\partial)/(\partial x)(ysin(xy)-2xy)	\frac{\partial\:}{\partial\:x}(y\sin(xy)-2xy)
derivative of x^2-25In(x^2)	\frac{d}{dx}(x^{2}-25In(x^{2}))
integral of 2y^3	\int\:2y^{3}dy
derivative of 1/2 (2(7.5)+1)^{-1/2}	derivative\:\frac{1}{2}(2(7.5)+1)^{-\frac{1}{2}}
area 2-x^2,6-5x	area\:2-x^{2},6-5x
derivative of (sin(7x)^{ln(x)})	\frac{d}{dx}((\sin(7x))^{\ln(x)})
derivative of 1-e^{-x/3}	\frac{d}{dx}(1-e^{-\frac{x}{3}})
(5/(x^5))^'	(\frac{5}{x^{5}})^{\prime\:}
area 2y=3sqrt(x),y=3,2y+4x=7	area\:2y=3\sqrt{x},y=3,2y+4x=7
integral from 0 to pi/4 of 1+tan(x)	\int\:_{0}^{\frac{π}{4}}1+\tan(x)dx
derivative of (6x/(x^2-9))	\frac{d}{dx}(\frac{6x}{x^{2}-9})
y^'=(3x-2)(30x+29)	y^{\prime\:}=(3x-2)(30x+29)
implicit (dy)/(dx),9x^2+y^2=1	implicit\:\frac{dy}{dx},9x^{2}+y^{2}=1
limit as x approaches-infinity of x^2	\lim\:_{x\to\:-\infty\:}(x^{2})
(d^2y)/(dx^2)+2(dy)/(dx)=12x^2	\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}=12x^{2}
integral of ((2x+11))/(x^2+x-6)	\int\:\frac{(2x+11)}{x^{2}+x-6}dx
integral of 1/(xsqrt(49+x^2))	\int\:\frac{1}{x\sqrt{49+x^{2}}}dx
derivative of f(x)=sqrt(x)(5e^x-4x^4)	derivative\:f(x)=\sqrt{x}(5e^{x}-4x^{4})
integral of 2^{x^2}	\int\:2^{x^{2}}dx
inverse oflaplace 1/((s^2+6pis+pi^2))	inverselaplace\:\frac{1}{(s^{2}+6πs+π^{2})}
area ((x-4)^2+1/2),[2,4]	area\:((x-4)^{2}+\frac{1}{2}),[2,4]
integral of (4x+10)/(x^3+x)	\int\:\frac{4x+10}{x^{3}+x}dx
(dy)/(dx)+0.7y=18.2	\frac{dy}{dx}+0.7y=18.2
integral of (e^x)/(sqrt(1-49e^{2x))}	\int\:\frac{e^{x}}{\sqrt{1-49e^{2x}}}dx
integral of 2(2x-1)ln(x-1)	\int\:2(2x-1)\ln(x-1)dx
integral of (5x^3+10x)^3(3x^2+2)	\int\:(5x^{3}+10x)^{3}(3x^{2}+2)dx
derivative of x^5+5^x	derivative\:x^{5}+5^{x}

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