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Popular Calculus Problems

integral of sin^5(3x)	\int\:\sin^{5}(3x)dx
(dy)/(dt)-4/t*y=t^5	\frac{dy}{dt}-\frac{4}{t}\cdot\:y=t^{5}
integral of (cos(3pi)x)/2	\int\:\frac{\cos(3π)x}{2}dx
simplify 1/6 t^3	simplify\:\frac{1}{6}t^{3}
(\partial)/(\partial x)((x^3-y^2)^{(-1)})	\frac{\partial\:}{\partial\:x}((x^{3}-y^{2})^{(-1)})
3y^{''}-4y^'-15y=0,y(0)=-7,y^'(0)=-2	3y^{\prime\:\prime\:}-4y^{\prime\:}-15y=0,y(0)=-7,y^{\prime\:}(0)=-2
derivative of (9x^2-18x+18e^x)	\frac{d}{dx}((9x^{2}-18x+18)e^{x})
derivative of (x-1(x+1)(ln(900)-ln(x)))	\frac{d}{dx}((x-1)(x+1)(\ln(900)-\ln(x)))
inverse oflaplace 1/(s(s^2+9))	inverselaplace\:\frac{1}{s(s^{2}+9)}
tangent of f(x)=2cos(x)+cos^2(x)	tangent\:f(x)=2\cos(x)+\cos^{2}(x)
derivative of 7e^{-2x}	\frac{d}{dx}(7e^{-2x})
integral of 1/(sin^2(x)cos^2(x))	\int\:\frac{1}{\sin^{2}(x)\cos^{2}(x)}dx
derivative of 8/((1-x)^2)	derivative\:\frac{8}{(1-x)^{2}}
integral of 1	\int\:1dx
y^{''}+y=6e^{-t},y^'(0)=0,y(0)=0	y^{\prime\:\prime\:}+y=6e^{-t},y^{\prime\:}(0)=0,y(0)=0
area y=\|6x\|,y=x^2-7	area\:y=\left\|6x\right\|,y=x^{2}-7
sum from n=1 to infinity}(\sqrt{n of)/n	\sum\:_{n=1}^{\infty\:}\frac{\sqrt{n}}{n}
derivative of-y	derivative\:-y
derivative of 20cos(2x)	\frac{d}{dx}(20\cos(2x))
derivative of 2ln(3-x)	\frac{d}{dx}(2\ln(3-x))
derivative of x^1	\frac{d}{dx}(x^{1})
integral from-1 to 4 of \|x\|	\int\:_{-1}^{4}\left\|x\right\|dx
inverse oflaplace (2s+6)/(8s^2-2s-3)	inverselaplace\:\frac{2s+6}{8s^{2}-2s-3}
area y=2x^2,y^2= 1/2 x	area\:y=2x^{2},y^{2}=\frac{1}{2}x
y^'y^{-2}+xy^{-1}=x	y^{\prime\:}y^{-2}+xy^{-1}=x
derivative of (5x+2)/(12x+5)	derivative\:\frac{5x+2}{12x+5}
integral of (sqrt(9x^2-1))/(x^2)	\int\:\frac{\sqrt{9x^{2}-1}}{x^{2}}dx
derivative of (100/(x^2))	\frac{d}{dx}(\frac{100}{x^{2}})
integral of (sin(2x))/(sqrt(sin^2(x)-3))	\int\:\frac{\sin(2x)}{\sqrt{\sin^{2}(x)-3}}dx
integral of (x^2e^{x^3})	\int\:(x^{2}e^{x^{3}})dx
integral of arccos(2x)	\int\:\arccos(2x)dx
integral of cos(x)*cos(x)	\int\:\cos(x)\cdot\:\cos(x)dx
integral of tan^8(x)sec^4(x)	\int\:\tan^{8}(x)\sec^{4}(x)dx
tangent of y=4-x^2,(4,-12)	tangent\:y=4-x^{2},(4,-12)
integral of (6x)/((9x^2-4)^3)	\int\:\frac{6x}{(9x^{2}-4)^{3}}dx
(\partial}{\partial x}(xy*e^{(\frac{(-5x^2+5y^2))/2+1)})	\frac{\partial\:}{\partial\:x}(xy\cdot\:e^{(\frac{(-5x^{2}+5y^{2})}{2}+1)})
(dy)/(dx)=y^2(6-2x)	\frac{dy}{dx}=y^{2}(6-2x)
(\partial)/(\partial x)(ln(x/k))	\frac{\partial\:}{\partial\:x}(\ln(\frac{x}{k}))
derivative of (2-x(y-2)(3-x-y))	\frac{d}{dx}((2-x)(y-2)(3-x-y))
derivative of (3xy+7^2)	\frac{d}{dx}((3xy+7)^{2})
integral of x^2ln(x^4)	\int\:x^{2}\ln(x^{4})dx
derivative of (sin(x)^4)	\frac{d}{dx}((\sin(x))^{4})
(\partial)/(\partial x)(y^4cos(3x))	\frac{\partial\:}{\partial\:x}(y^{4}\cos(3x))
integral of (3x^2+2)/((x^3+2x+3)^5)	\int\:\frac{3x^{2}+2}{(x^{3}+2x+3)^{5}}dx
y^'=(x^2+y^2)/(x*y)	y^{\prime\:}=\frac{x^{2}+y^{2}}{x\cdot\:y}
derivative of cos(10x)	\frac{d}{dx}(\cos(10x))
xy^'+y^'-(x+1)cos(x)+y=0	xy^{\prime\:}+y^{\prime\:}-(x+1)\cos(x)+y=0
derivative of (e^{-x}+e^x^3)	\frac{d}{dx}((e^{-x}+e^{x})^{3})
integral of x/((x-3))	\int\:\frac{x}{(x-3)}dx
inverse oflaplace (s^2-1)/((s^2+1)^2)	inverselaplace\:\frac{s^{2}-1}{(s^{2}+1)^{2}}
derivative of ((ax+by(x))/(cx+dy))	\frac{d}{dx}(\frac{(ax+by(x))}{cx+dy})
(dx)/(dt)=5x(9-x)	\frac{dx}{dt}=5x(9-x)
derivative of ae^x	\frac{d}{dx}(ae^{x})
integral of cos^2(1/3)x	\int\:\cos^{2}(\frac{1}{3})xdx
(\partial)/(\partial x)(x+y-1)	\frac{\partial\:}{\partial\:x}(x+y-1)
integral of (t^2+1)^2	\int\:(t^{2}+1)^{2}dt
integral from-infinity to 9 of re^{r/3}	\int\:_{-\infty\:}^{9}re^{\frac{r}{3}}dr
integral of 4/(xsqrt(1+2x))	\int\:\frac{4}{x\sqrt{1+2x}}dx
(\partial)/(\partial x)(x*e^{-y/x})	\frac{\partial\:}{\partial\:x}(x\cdot\:e^{-\frac{y}{x}})
sum from n=1 to infinity}((x)^{n-1 of)/x	\sum\:_{n=1}^{\infty\:}\frac{(x)^{n-1}}{x}
integral of cos^2(t)sin^2(t)	\int\:\cos^{2}(t)\sin^{2}(t)dt
integral of z^3cos(x)+2xy^2	\int\:z^{3}\cos(x)+2xy^{2}dx
(\partial)/(\partial x)(6y^2-x^2+3)	\frac{\partial\:}{\partial\:x}(6y^{2}-x^{2}+3)
integral from 0 to 5 of pi(25x^2-x^4)	\int\:_{0}^{5}π(25x^{2}-x^{4})dx
integral of (6+u)/u	\int\:\frac{6+u}{u}du
d/(dy)(y/(sqrt(x^2+y^2)))	\frac{d}{dy}(\frac{y}{\sqrt{x^{2}+y^{2}}})
integral of x^2-2x-8	\int\:x^{2}-2x-8dx
integral from 3 to 10 of (100-y^2)(y+2)	\int\:_{3}^{10}(100-y^{2})(y+2)dy
derivative of f(x)=x^3-5	derivative\:f(x)=x^{3}-5
derivative of 1/(x^4+x^2+1)	\frac{d}{dx}(\frac{1}{x^{4}+x^{2}+1})
(dy)/(dx)=((2x^4+2y))/(-2x-3y)	\frac{dy}{dx}=\frac{(2x^{4}+2y)}{-2x-3y}
derivative of-2sin(2t)	derivative\:-2\sin(2t)
integral of 4/(3+4x)	\int\:\frac{4}{3+4x}dx
integral from 1 to 49 of 1/(2x)	\int\:_{1}^{49}\frac{1}{2x}dx
derivative of (x^2/3)	\frac{d}{dx}(\frac{x^{2}}{3})
laplacetransform t*e^{-5t}	laplacetransform\:t\cdot\:e^{-5t}
derivative of f(x)=5x+4	derivative\:f(x)=5x+4
limit as x approaches-7 of 1/(x^2(x+7))	\lim\:_{x\to\:-7}(\frac{1}{x^{2}(x+7)})
(81-x^2)y^'=7y	(81-x^{2})y^{\prime\:}=7y
derivative of 8/(e^x+e^{-x})	\frac{d}{dx}(\frac{8}{e^{x}+e^{-x}})
integral of (e^{3x})/(sqrt(4-4e^{6x))}	\int\:\frac{e^{3x}}{\sqrt{4-4e^{6x}}}dx
d/(dz)((2z+3i)(z-i))	\frac{d}{dz}((2z+3i)(z-i))
limit as x approaches 0 of (3x)/(sin(x))	\lim\:_{x\to\:0}(\frac{3x}{\sin(x)})
integral of (sqrt(x)+1)(x-sqrt(x)+1)	\int\:(\sqrt{x}+1)(x-\sqrt{x}+1)dx
integral of tcos(t^2)	\int\:t\cos(t^{2})dt
integral of-1/(2x^2)	\int\:-\frac{1}{2x^{2}}dx
derivative of f(x)=(1/(2x+3))^3	derivative\:f(x)=(\frac{1}{2x+3})^{3}
tangent of 8/(x^2+4)(2.1)	tangent\:\frac{8}{x^{2}+4}(2.1)
integral of 1/(x^{1/5)+2}	\int\:\frac{1}{x^{\frac{1}{5}}+2}dx
integral from 1 to 8 of \sqrt[3]{x}	\int\:_{1}^{8}\sqrt[3]{x}dx
derivative of 2x^2-2	\frac{d}{dx}(2x^{2}-2)
tangent of f(x)=4x^2,\at x=9	tangent\:f(x)=4x^{2},\at\:x=9
taylor 4x^{-1}	taylor\:4x^{-1}
area-4x^2+6.25x+8,2.5x+7	area\:-4x^{2}+6.25x+8,2.5x+7
integral of (sec(x)-2xtan(x)-2x)	\int\:(\sec(x)-2x\tan(x)-2x)dx
derivative of-2ln(3/2 x)	\frac{d}{dx}(-2\ln(\frac{3}{2}x))
7y^'+5y=2e^{3x}	7y^{\prime\:}+5y=2e^{3x}
derivative of f(x)=(e^x)/(x^2+9)	derivative\:f(x)=\frac{e^{x}}{x^{2}+9}
d/(dt)(t^{sqrt(3t)})	\frac{d}{dt}(t^{\sqrt{3t}})
limit as x approaches 2 of (x^3-x)/(x-2)	\lim\:_{x\to\:2}(\frac{x^{3}-x}{x-2})

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