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Popular Calculus Problems

integral from 0 to 1 of x^2sqrt(6x+8)	\int\:_{0}^{1}x^{2}\sqrt{6x+8}dx
integral of ((7x^2+5x+7))/((x^2+1)^2)	\int\:\frac{(7x^{2}+5x+7)}{(x^{2}+1)^{2}}dx
derivative of (16/(x^2)-4/x)	\frac{d}{dx}(\frac{16}{x^{2}}-\frac{4}{x})
derivative of f(x)=(a^{1/x}+b^{1/x})^x	derivative\:f(x)=(a^{\frac{1}{x}}+b^{\frac{1}{x}})^{x}
integral of (x^3)/(sqrt(5x^2+\sqrt{2))}	\int\:\frac{x^{3}}{\sqrt{5x^{2}+\sqrt{2}}}dx
inverse oflaplace 8/(s^2+9)	inverselaplace\:\frac{8}{s^{2}+9}
(d^2)/(dx^2)((x-4)/(3x-x^2))	\frac{d^{2}}{dx^{2}}(\frac{x-4}{3x-x^{2}})
limit as x approaches 0-of arcsin(e^x)	\lim\:_{x\to\:0-}(\arcsin(e^{x}))
(\partial)/(\partial a)(ab)	\frac{\partial\:}{\partial\:a}(ab)
integral from-infinity to 0 of xe^{4x}	\int\:_{-\infty\:}^{0}xe^{4x}dx
integral of x^4(1-x^5)^7	\int\:x^{4}(1-x^{5})^{7}dx
(\partial)/(\partial x)(wsqrt(x+2y+3z))	\frac{\partial\:}{\partial\:x}(w\sqrt{x+2y+3z})
limit as x approaches 2 of ([x-2])/(x-2)	\lim\:_{x\to\:2}(\frac{[x-2]}{x-2})
derivative of (a^2-x^3/(b^2))	\frac{d}{dx}(\frac{a^{2}-x^{3}}{b^{2}})
area x=7y^2,x=8+5y^2	area\:x=7y^{2},x=8+5y^{2}
derivative of (2x)/(x+2)	derivative\:\frac{2x}{x+2}
integral of (x^2+1)/(x^2)	\int\:\frac{x^{2}+1}{x^{2}}dx
xe^ydy+(x^2+1)/y dx=0	xe^{y}dy+\frac{x^{2}+1}{y}dx=0
derivative of sqrt((1-2x/(1+2x)))	\frac{d}{dx}(\sqrt{\frac{1-2x}{1+2x}})
derivative of x^2sin(x-xcos(x))	\frac{d}{dx}(x^{2}\sin(x)-x\cos(x))
derivative of (3x^3+2x)(x-2)(x+4)	derivative\:(3x^{3}+2x)(x-2)(x+4)
cos(x)dx-sin(y)dy=0	\cos(x)dx-\sin(y)dy=0
integral of arcsin(x	\int\:\arcsin(d)xdx
limit as n approaches infinity of 1-n	\lim\:_{n\to\:\infty\:}(1-n)
integral of (-(\sqrt[3]{x^2})/5)	\int\:(-\frac{\sqrt[3]{x^{2}}}{5})dx
(dy)/(dx)=(3-y)/(2x)	\frac{dy}{dx}=\frac{3-y}{2x}
derivative of y=3tan(4x)	derivative\:y=3\tan(4x)
integral of cos^2(x)-cos^4(x)	\int\:\cos^{2}(x)-\cos^{4}(x)dx
integral of (cos(x))/((2-3sin(x))^4)	\int\:\frac{\cos(x)}{(2-3\sin(x))^{4}}dx
derivative of ln((6-7x^4^6))	\frac{d}{dx}(\ln((6-7x^{4})^{6}))
derivative of ln(5x^2+9y^2)	derivative\:\ln(5x^{2}+9y^{2})
(\partial)/(\partial x)(sin(pi))	\frac{\partial\:}{\partial\:x}(\sin(π))
integral of (e^x)/((e^x+1)^2)	\int\:\frac{e^{x}}{(e^{x}+1)^{2}}dx
integral of e^{2x}-x^2-1	\int\:e^{2x}-x^{2}-1dx
derivative of cos(sqrt(2)x)	\frac{d}{dx}(\cos(\sqrt{2}x))
y^'=y(xy^2+1)	y^{\prime\:}=y(xy^{2}+1)
integral of 4sin^6(x)cos^3(x)	\int\:4\sin^{6}(x)\cos^{3}(x)dx
(y+sqrt(x^2-y^2))dx-xdy=0	(y+\sqrt{x^{2}-y^{2}})dx-xdy=0
integral of 4x^2e^x	\int\:4x^{2}e^{x}dx
tangent of f(x)=x^3-6x^2+12x-9	tangent\:f(x)=x^{3}-6x^{2}+12x-9
(\partial)/(\partial y)(-0.2y+23)	\frac{\partial\:}{\partial\:y}(-0.2y+23)
(\partial)/(\partial x)(-5xy(9-x-y))	\frac{\partial\:}{\partial\:x}(-5xy(9-x-y))
integral of 1/((16x^4+8x^2+1))	\int\:\frac{1}{(16x^{4}+8x^{2}+1)}dx
integral from 0 to 2 of 2pi(x+1)(4-2x)	\int\:_{0}^{2}2π(x+1)(4-2x)dx
integral from 0 to 1 of (3/(1+t^2))	\int\:_{0}^{1}(\frac{3}{1+t^{2}})dt
derivative of 3xcos(x)	derivative\:3x\cos(x)
tangent of-4-9x^2	tangent\:-4-9x^{2}
2(d^2y)/(dx^2)+11(dy)/(dx)-6y=8x	2\frac{d^{2}y}{dx^{2}}+11\frac{dy}{dx}-6y=8x
(x^2-4)(dy)/(dx)+4y=(x+2)^2	(x^{2}-4)\frac{dy}{dx}+4y=(x+2)^{2}
limit as x approaches 2 of x^3+5x^2-7x+1	\lim\:_{x\to\:2}(x^{3}+5x^{2}-7x+1)
derivative of-(25/((1+5x)^2))	\frac{d}{dx}(-\frac{25}{(1+5x)^{2}})
derivative of x/5+5/x	derivative\:\frac{x}{5}+\frac{5}{x}
integral of 6x^3sqrt(3x^4+2)	\int\:6x^{3}\sqrt{3x^{4}+2}dx
integral of xln(3+x)	\int\:x\ln(3+x)dx
derivative of (-9x^3+5x^2)^4	derivative\:(-9x^{3}+5x^{2})^{4}
integral of (4sec(x)tan(x)+3sec^2(x))	\int\:(4\sec(x)\tan(x)+3\sec^{2}(x))dx
(\partial)/(\partial x)(-y^2)	\frac{\partial\:}{\partial\:x}(-y^{2})
integral of u^{-3} 1/2	\int\:u^{-3}\frac{1}{2}du
(dy)/(dx)=xe^{-x}	\frac{dy}{dx}=xe^{-x}
integral from 0 to 7 of 5/3 x	\int\:_{0}^{7}\frac{5}{3}xdx
inverse oflaplace-1/(s^2+(5)^2)	inverselaplace\:-\frac{1}{s^{2}+(5)^{2}}
integral from-3 to 0 of sqrt(9-x^2)	\int\:_{-3}^{0}\sqrt{9-x^{2}}dx
inverse oflaplace (3s-1)/((s^2+2s+5))	inverselaplace\:\frac{3s-1}{(s^{2}+2s+5)}
(dy)/(dx)=3(y^2+1),y(pi/4)=1	\frac{dy}{dx}=3(y^{2}+1),y(\frac{π}{4})=1
y^'-y=2te^{2t}	y^{\prime\:}-y=2te^{2t}
(\partial)/(\partial y)(2xe^{x^2-y^2})	\frac{\partial\:}{\partial\:y}(2xe^{x^{2}-y^{2}})
integral of ye^{-y}	\int\:ye^{-y}dy
derivative of cos^2(sin(4x))	\frac{d}{dx}(\cos^{2}(\sin(4x)))
y^{''}+5y^'+6y=2e^x,y(0)=1,y^'(0)=-1	y^{\prime\:\prime\:}+5y^{\prime\:}+6y=2e^{x},y(0)=1,y^{\prime\:}(0)=-1
integral of 4sin(5x)+5cos(3x)	\int\:4\sin(5x)+5\cos(3x)dx
(dy)/(dt)=2y-t	\frac{dy}{dt}=2y-t
derivative of (1+x^2^5)	\frac{d}{dx}((1+x^{2})^{5})
derivative of (-11)/(\sqrt[3]{x)}	derivative\:\frac{-11}{\sqrt[3]{x}}
derivative of sin(2x*2)	\frac{d}{dx}(\sin(2x)\cdot\:2)
derivative of ae^v+b/v+c/(v^2)	\frac{d}{dx}(ae^{v}+\frac{b}{v}+\frac{c}{v^{2}})
(\partial)/(\partial u)(sqrt(u^9+v^7))	\frac{\partial\:}{\partial\:u}(\sqrt{u^{9}+v^{7}})
integral of (cos(x))^{-1}	\int\:(\cos(x))^{-1}dx
derivative of x^{1/2}(3x^2-35x+90)	\frac{d}{dx}(x^{\frac{1}{2}}(3x^{2}-35x+90))
(d^2)/(dx^2)(\sqrt[3]{(x^2-1)^2})	\frac{d^{2}}{dx^{2}}(\sqrt[3]{(x^{2}-1)^{2}})
integral of 1/((1+x)^2)	\int\:\frac{1}{(1+x)^{2}}dx
derivative of 5^5	\frac{d}{dx}(5^{5})
limit as x approaches 2+of x^2+2	\lim\:_{x\to\:2+}(x^{2}+2)
d/(dθ)(sin^2(θ/2))	\frac{d}{dθ}(\sin^{2}(\frac{θ}{2}))
tangent of f(x)=x^2(2x+1/x),\at x=3	tangent\:f(x)=x^{2}(2x+\frac{1}{x}),\at\:x=3
integral of 7x-sqrt(x)	\int\:7x-\sqrt{x}dx
derivative of y=ln(-3x^6)	derivative\:y=\ln(-3x^{6})
(1+y^2)dx-(x^2+1)dy=0	(1+y^{2})dx-(x^{2}+1)dy=0
(\partial)/(\partial x)((-y^4)/(4x^4))	\frac{\partial\:}{\partial\:x}(\frac{-y^{4}}{4x^{4}})
integral of (1/(1-x))	\int\:(\frac{1}{1-x})dx
tangent of f(x)=2x^2+2x,(-2,-6)	tangent\:f(x)=2x^{2}+2x,(-2,-6)
integral from 0 to 2 of ln(1+x^4)	\int\:_{0}^{2}\ln(1+x^{4})dx
integral of 3^{-x}	\int\:3^{-x}dx
x^{''}=-x+3x^'	x^{\prime\:\prime\:}=-x+3x^{\prime\:}
integral from 0 to 1 of 2pix(sqrt(x))	\int\:_{0}^{1}2πx(\sqrt{x})dx
integral of 2/9 (x^2)/(x^5)	\int\:\frac{2}{9}\frac{x^{2}}{x^{5}}dx
integral of 1/((x+1)(x+2)(x+3))	\int\:\frac{1}{(x+1)(x+2)(x+3)}dx
(\partial)/(\partial x)(9-x^2+xy-4y^2)	\frac{\partial\:}{\partial\:x}(9-x^{2}+xy-4y^{2})
integral of 1/(cos(x)-1)	\int\:\frac{1}{\cos(x)-1}dx
limit as x approaches 0 of (5^x-1)/x	\lim\:_{x\to\:0}(\frac{5^{x}-1}{x})
derivative of y=x^e	derivative\:y=x^{e}

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