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Popular Calculus Problems

integral of 3x^2cos(6x)	\int\:3x^{2}\cos(6x)dx
derivative of ln(x^2-1/(x^2)-5)	\frac{d}{dx}(\ln(x^{2})-\frac{1}{x^{2}}-5)
derivative of (x^2/(x^2-5))	\frac{d}{dx}(\frac{x^{2}}{x^{2}-5})
integral of ((x-3)^2)/(x^2-x+2)	\int\:\frac{(x-3)^{2}}{x^{2}-x+2}dx
derivative of 2^zlog_{2}(z)	derivative\:2^{z}\log_{2}(z)
y^'+((3y)/((300-t)))=4	y^{\prime\:}+(\frac{3y}{(300-t)})=4
integral of (sqrt(64x^2-1))/x	\int\:\frac{\sqrt{64x^{2}-1}}{x}dx
(\partial)/(\partial x)(e^{x^2y}+x^2y)	\frac{\partial\:}{\partial\:x}(e^{x^{2}y}+x^{2}y)
derivative of-y/(x^2)	\frac{d}{dx}(-\frac{y}{x^{2}})
(\partial)/(\partial x)(x^5+xy^7+6)	\frac{\partial\:}{\partial\:x}(x^{5}+xy^{7}+6)
derivative of \sqrt[3]{9x^2+7}	\frac{d}{dx}(\sqrt[3]{9x^{2}+7})
tangent of f(x)=4cos(x),(pi/3 ,2)	tangent\:f(x)=4\cos(x),(\frac{π}{3},2)
(\partial)/(\partial w)(te^{w/t})	\frac{\partial\:}{\partial\:w}(te^{\frac{w}{t}})
integral of (xe^{3x})/2	\int\:\frac{xe^{3x}}{2}dx
integral from k to 2k of 2/((2x-k)^2)	\int\:_{k}^{2k}\frac{2}{(2x-k)^{2}}dx
integral of (sec(x))/(sec(x)-cos(x))	\int\:\frac{\sec(x)}{\sec(x)-\cos(x)}dx
derivative of-18	\frac{d}{dx}(-18)
integral of-1/5 e^{-5x}	\int\:-\frac{1}{5}e^{-5x}dx
integral of (sqrt(x))/(2x)	\int\:\frac{\sqrt{x}}{2x}dx
derivative of x^4+3x^3-x^2	\frac{d}{dx}(x^{4}+3x^{3}-x^{2})
inverse oflaplace (s+1)/((s^2-4s)(s+5))	inverselaplace\:\frac{s+1}{(s^{2}-4s)(s+5)}
limit as x approaches 2 of ln(x^2-4)	\lim\:_{x\to\:2}(\ln(x^{2}-4))
derivative of (e^x/(x*cos(x)))	\frac{d}{dx}(\frac{e^{x}}{x\cdot\:\cos(x)})
f^{''}+16f=sin(2x)	f^{\prime\:\prime\:}+16f=\sin(2x)
integral from 6 to 12 of sqrt(144-x^2)	\int\:_{6}^{12}\sqrt{144-x^{2}}dx
x^2y^{''}-6y=0,y(1)=6,y^'(1)=-2	x^{2}y^{\prime\:\prime\:}-6y=0,y(1)=6,y^{\prime\:}(1)=-2
(\partial)/(\partial x)(e^{xy}y^2+x/y)	\frac{\partial\:}{\partial\:x}(e^{xy}y^{2}+\frac{x}{y})
integral of e^{-(x^2)/2}	\int\:e^{-\frac{x^{2}}{2}}dx
integral from 0 to 1 of (x^4+3)/x	\int\:_{0}^{1}\frac{x^{4}+3}{x}dx
derivative of y= 1/((3x+8)^2)	derivative\:y=\frac{1}{(3x+8)^{2}}
limit as x approaches-3 of 5x	\lim\:_{x\to\:-3}(5x)
derivative of-2sqrt(9s^2+1)	derivative\:-2\sqrt{9s^{2}+1}
limit as x approaches 2-of f(x)	\lim\:_{x\to\:2-}(f(x))
derivative of sqrt((x^27^x^9))	\frac{d}{dx}(\sqrt{(x^{2}7^{x})^{9}})
derivative of e^{x^2+x}	\frac{d}{dx}(e^{x^{2}+x})
integral of sin(5x)cos(5x)	\int\:\sin(5x)\cos(5x)dx
integral of 2 1/x	\int\:2\frac{1}{x}dx
integral of e^{-7x}tan(e^{-7x})	\int\:e^{-7x}\tan(e^{-7x})dx
xy^'+2yln(x)=3	xy^{\prime\:}+2y\ln(x)=3
integral from 1 to 3 of (x^2+8)/(4x-x^2)	\int\:_{1}^{3}\frac{x^{2}+8}{4x-x^{2}}dx
y^'=xsqrt(y)	y^{\prime\:}=x\sqrt{y}
derivative of y=ln(x+sqrt(x^2-1))	derivative\:y=\ln(x+\sqrt{x^{2}-1})
limit as x approaches 0+of ln(1/x)	\lim\:_{x\to\:0+}(\ln(\frac{1}{x}))
limit as x approaches 1 of 7\|x+1\|-4	\lim\:_{x\to\:1}(7\left\|x+1\right\|-4)
derivative of y=(x-1)(x^2+x+1)	derivative\:y=(x-1)(x^{2}+x+1)
(dy)/(dx)=(2x)/(y+1)	\frac{dy}{dx}=\frac{2x}{y+1}
integral from 1 to 1000 of (25)/(x^3)	\int\:_{1}^{1000}\frac{25}{x^{3}}dx
x^2y^'+2xy=ln(x),y(1)=2	x^{2}y^{\prime\:}+2xy=\ln(x),y(1)=2
tangent of ((x^2))/(x+2)	tangent\:\frac{(x^{2})}{x+2}
limit as x approaches 0 of (cos(pi/2-x))/x	\lim\:_{x\to\:0}(\frac{\cos(\frac{π}{2}-x)}{x})
sum from n=2 to infinity of 5*(-3/4)^n	\sum\:_{n=2}^{\infty\:}5\cdot\:(-\frac{3}{4})^{n}
y^{''}+5y^'+4y=t^2e^{7t}	y^{\prime\:\prime\:}+5y^{\prime\:}+4y=t^{2}e^{7t}
integral from 0 to ln(5) of e^x-e^{-2x}	\int\:_{0}^{\ln(5)}e^{x}-e^{-2x}dx
integral from 0 to 6 of (6t)/((t-7)^2)	\int\:_{0}^{6}\frac{6t}{(t-7)^{2}}dt
derivative of (x^2/(1-y^2))	\frac{d}{dx}(\frac{x^{2}}{1-y^{2}})
derivative of (x+3)(x-5)^7	derivative\:(x+3)(x-5)^{7}
limit as x approaches+0 of (x^2-5)/(x-2)	\lim\:_{x\to\:+0}(\frac{x^{2}-5}{x-2})
(dy)/(sqrt(1-y^2))=dx	\frac{dy}{\sqrt{1-y^{2}}}=dx
(dy)/(dt)=(8ty)/(t^2+1),y(0)=-2	\frac{dy}{dt}=\frac{8ty}{t^{2}+1},y(0)=-2
integral of 15x^2	\int\:15x^{2}dx
integral of sec^2(3x)e^{tan(3x)-2}	\int\:\sec^{2}(3x)e^{\tan(3x)-2}dx
integral of 1/(4+u^2)	\int\:\frac{1}{4+u^{2}}du
xy^'+y=e^x,y(1)=2	xy^{\prime\:}+y=e^{x},y(1)=2
derivative of sqrt(cos^2(x-sin^2(x)))	\frac{d}{dx}(\sqrt{\cos^{2}(x)-\sin^{2}(x)})
derivative of arctan((x+1/(x-1)))	\frac{d}{dx}(\arctan(\frac{x+1}{x-1}))
integral of 1/((x+1)^3(x+2))	\int\:\frac{1}{(x+1)^{3}(x+2)}dx
derivative of f(x)=(2x-2)^4(x^2+x+1)^5	derivative\:f(x)=(2x-2)^{4}(x^{2}+x+1)^{5}
(\partial)/(\partial x)(5ye^x)	\frac{\partial\:}{\partial\:x}(5ye^{x})
tangent of y=6sqrt(x),(1,6)	tangent\:y=6\sqrt{x},(1,6)
integral of sin(x+7)	\int\:\sin(x+7)dx
slope ofintercept (-1.1)(-4.1)	slopeintercept\:(-1.1)(-4.1)
integral of (\sqrt[3]{x})/2	\int\:\frac{\sqrt[3]{x}}{2}dx
(d^2)/(dx^2)(7x^{-3}+5t^{-8/3})	\frac{d^{2}}{dx^{2}}(7x^{-3}+5t^{-\frac{8}{3}})
integral from 0 to 1 of (3x)^2	\int\:_{0}^{1}(3x)^{2}dx
inverse oflaplace (4s-18)/(s^2-6s+10)	inverselaplace\:\frac{4s-18}{s^{2}-6s+10}
derivative of y=sqrt(x)+5	derivative\:y=\sqrt{x}+5
(dy)/(dx)+ay=0	\frac{dy}{dx}+ay=0
limit as x approaches-2 of 3x^4+2x^2-x+1	\lim\:_{x\to\:-2}(3x^{4}+2x^{2}-x+1)
y^{''}-4y^'+4y=t^3,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=t^{3},y(0)=1,y^{\prime\:}(0)=0
(dy)/(dx)=((y-x+1))/(y-x-6)	\frac{dy}{dx}=\frac{(y-x+1)}{y-x-6}
y^{''''}+5y^{''}+4y=0,y(0)=0	y^{\prime\:\prime\:\prime\:\prime\:}+5y^{\prime\:\prime\:}+4y=0,y(0)=0
ydx-4xdy=y^6	ydx-4xdy=y^{6}
integral of (x^3)/3 1/x	\int\:\frac{x^{3}}{3}\frac{1}{x}dx
derivative of (x-2)^{-1}	derivative\:(x-2)^{-1}
integral of (2x^2+x-3)	\int\:(2x^{2}+x-3)dx
integral of (sin^5(x))(cos(x))^2x	\int\:(\sin^{5}(x))(\cos(x))^{2}xdx
laplacetransform 20	laplacetransform\:20
integral of-9ln(x)	\int\:-9\ln(x)dx
integral of (x-2)sqrt(8-x)	\int\:(x-2)\sqrt{8-x}dx
derivative of sqrt(9-t)	derivative\:\sqrt{9-t}
derivative of (xy/(sqrt(x^2+y^2)))	\frac{d}{dx}(\frac{xy}{\sqrt{x^{2}+y^{2}}})
sum from n=0 to infinity of 4/(5^{n-1)}	\sum\:_{n=0}^{\infty\:}\frac{4}{5^{n-1}}
limit as x approaches-2-of x/(x+2)	\lim\:_{x\to\:-2-}(\frac{x}{x+2})
integral of 1/((e^x-3)^2)	\int\:\frac{1}{(e^{x}-3)^{2}}dx
limit as x approaches 64 of x^{2/3}	\lim\:_{x\to\:64}(x^{\frac{2}{3}})
laplacetransform e^{-t}*sin(t)	laplacetransform\:e^{-t}\cdot\:\sin(t)
integral of xln(x))	\int\:xd(\ln(x))dx
integral of x/(sqrt(5+x))	\int\:\frac{x}{\sqrt{5+x}}dx
derivative of ((5x-3)/(4x-3/x))	\frac{d}{dx}(\frac{(5x-3)}{4x-\frac{3}{x}})
derivative of sin^5((x^2+1^7))	\frac{d}{dx}(\sin^{5}((x^{2}+1)^{7}))

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