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Popular Calculus Problems

integral of cos^4(5x)sin(5x)	\int\:\cos^{4}(5x)\sin(5x)dx
integral of 1/(441-400x^2)	\int\:\frac{1}{441-400x^{2}}dx
derivative of 1/3*(x^2+2^{3/2})	\frac{d}{dx}(\frac{1}{3}\cdot\:(x^{2}+2)^{\frac{3}{2}})
area x^3-6x^2+8x,x^2-4x	area\:x^{3}-6x^{2}+8x,x^{2}-4x
t^4y^{''}+t^3y^'=0	t^{4}y^{\prime\:\prime\:}+t^{3}y^{\prime\:}=0
integral of 2/(pi(1+x^2))	\int\:\frac{2}{π(1+x^{2})}dx
integral of (-x^2+11x-18)/(x^2)	\int\:\frac{-x^{2}+11x-18}{x^{2}}dx
integral of x^{5/7}	\int\:x^{\frac{5}{7}}dx
integral of 3cos^3(4x)	\int\:3\cos^{3}(4x)dx
integral of x^4e^{(x^5-2)}	\int\:x^{4}e^{(x^{5}-2)}dx
xy^'+3y=8x^2-6x	xy^{\prime\:}+3y=8x^{2}-6x
derivative of ((x+1^2)/(1+x^2))	\frac{d}{dx}(\frac{(x+1)^{2}}{1+x^{2}})
integral of (e^x+1)^2e^x	\int\:(e^{x}+1)^{2}e^{x}dx
4x+12,8-x^2,x=-2,x=6	4x+12,8-x^{2},x=-2,x=6
(dy)/(dx)=x+3y	\frac{dy}{dx}=x+3y
integral from-infinity to 16 of re^{r/4}	\int\:_{-\infty\:}^{16}re^{\frac{r}{4}}dr
integral of (1-x^2)^{-1/2}	\int\:(1-x^{2})^{-\frac{1}{2}}dx
derivative of 100x^{3/2}	\frac{d}{dx}(100x^{\frac{3}{2}})
sum from n=1 to infinity of (4/9)^{2n+1}	\sum\:_{n=1}^{\infty\:}(\frac{4}{9})^{2n+1}
tangent of f(x)=x^2+x,\at x=2	tangent\:f(x)=x^{2}+x,\at\:x=2
y^{''}+3y^'+3y=0	y^{\prime\:\prime\:}+3y^{\prime\:}+3y=0
derivative of (2sqrt({f)(x})/(x^2+1))	\frac{d}{dx}(\frac{2\sqrt{{f}(x)}}{x^{2}+1})
(dy)/(dx)+3xy^3=0	\frac{dy}{dx}+3xy^{3}=0
integral from 0 to r of xarcsin(x/(2r))	\int\:_{0}^{r}x\arcsin(\frac{x}{2r})dx
integral of (sec(x)+cos(x))/(8cos(x))	\int\:\frac{\sec(x)+\cos(x)}{8\cos(x)}dx
(\partial)/(\partial x)(ln(x^2+1))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+1))
limit as x approaches 1+of arctan(ln(x))	\lim\:_{x\to\:1+}(\arctan(\ln(x)))
derivative of (9x)/(3x+7)	derivative\:\frac{9x}{3x+7}
integral of sin^2(2x)sin(x)	\int\:\sin^{2}(2x)\sin(x)dx
integral of 3\sqrt[3]{x^2}	\int\:3\sqrt[3]{x^{2}}dx
derivative of sin(tan(9x))	derivative\:\sin(\tan(9x))
integral of 1/(1^2+2x^2)	\int\:\frac{1}{1^{2}+2x^{2}}dx
integral of (x^3-5x^2+3x+14)/(x-3)	\int\:\frac{x^{3}-5x^{2}+3x+14}{x-3}dx
tangent of f(x)=e^{-3x},(0,1)	tangent\:f(x)=e^{-3x},(0,1)
(dx)/(dt)=5x(6-x)	\frac{dx}{dt}=5x(6-x)
(dy)/(dx)+3y=50	\frac{dy}{dx}+3y=50
(dy)/(dx)= y/x+x/(y^5)	\frac{dy}{dx}=\frac{y}{x}+\frac{x}{y^{5}}
integral of (12u)/(sqrt(u(u-8)))	\int\:\frac{12u}{\sqrt{u(u-8)}}du
sum from k=0 to infinity of (k+1)x^k	\sum\:_{k=0}^{\infty\:}(k+1)x^{k}
derivative of 5x^2e^{3x}	derivative\:5x^{2}e^{3x}
limit as x approaches-pi/4+of-sec(2x)	\lim\:_{x\to\:-\frac{π}{4}+}(-\sec(2x))
x*(dy)/(dx)=y+sqrt(x^2-y^2)	x\cdot\:\frac{dy}{dx}=y+\sqrt{x^{2}-y^{2}}
x(x+5y)((dy)/(dx))+(y(3x+5y))=0	x(x+5y)(\frac{dy}{dx})+(y(3x+5y))=0
integral of (1/(sin(x)))	\int\:(\frac{1}{\sin(x)})dx
tangent of (x+2)^2+(y-3)^2=37,(-8,2)	tangent\:(x+2)^{2}+(y-3)^{2}=37,(-8,2)
tangent of f(x)=x^3+2x,\at x=-1	tangent\:f(x)=x^{3}+2x,\at\:x=-1
derivative of (1+sqrt(x)/(1-sqrt(x)))	\frac{d}{dx}(\frac{1+\sqrt{x}}{1-\sqrt{x}})
derivative of f(x)=x\|x\|	derivative\:f(x)=x\left\|x\right\|
derivative of f(x)=5x-4	derivative\:f(x)=5x-4
integral from 1/3 to 5 of 12xln(3x)	\int\:_{\frac{1}{3}}^{5}12x\ln(3x)dx
integral of tan^2(xco)s^3x	\int\:\tan^{2}(xco)s^{3}xdx
limit as x approaches-2 of (-3)/(x+2)	\lim\:_{x\to\:-2}(\frac{-3}{x+2})
integral of e^{x+3e^x}	\int\:e^{x+3e^{x}}dx
(d^2y)/(dx^2)-9y=0	\frac{d^{2}y}{dx^{2}}-9y=0
(\partial)/(\partial x)(a-bx-c/y+d x/y)	\frac{\partial\:}{\partial\:x}(a-bx-\frac{c}{y}+d\frac{x}{y})
limit as x approaches 2 of 2x^2-x+2	\lim\:_{x\to\:2}(2x^{2}-x+2)
(x-y)dx+(x)dy=0	(x-y)dx+(x)dy=0
y^'+3y=e^{2x}+1	y^{\prime\:}+3y=e^{2x}+1
integral of 2(2+x^2)^{3/2}x	\int\:2(2+x^{2})^{\frac{3}{2}}xdx
slope of (5-2)(58)	slope\:(5-2)(58)
integral of (2x)/y	\int\:\frac{2x}{y}dx
derivative of y=7e^xcos(x)	derivative\:y=7e^{x}\cos(x)
derivative of sin(3x)	derivative\:\sin(3x)
slope of (8.17)(3.17)	slope\:(8.17)(3.17)
derivative of f(x)=(sin(x))/x	derivative\:f(x)=\frac{\sin(x)}{x}
derivative of x^3-9x^2+24x+1	\frac{d}{dx}(x^{3}-9x^{2}+24x+1)
integral of (x+4)^2(x-2)	\int\:(x+4)^{2}(x-2)dx
f(x)=arcsec(x)+arccsc(x)	f(x)=\arcsec(x)+\arccsc(x)
derivative of (x^3/(30)+5/(2x))	\frac{d}{dx}(\frac{x^{3}}{30}+\frac{5}{2x})
integral of cot^3(7x)	\int\:\cot^{3}(7x)dx
R(a)=(5a+1)^2	R(a)=(5a+1)^{2}
derivative of y*e^x	\frac{d}{dx}(y\cdot\:e^{x})
derivative of (54/((1+3x)^3))	\frac{d}{dx}(\frac{54}{(1+3x)^{3}})
y^'=(1-2t)y	y^{\prime\:}=(1-2t)y
derivative of xcot(5/(x^2))	\frac{d}{dx}(x\cot(\frac{5}{x^{2}}))
tangent of (x^2)/(x-6)	tangent\:\frac{x^{2}}{x-6}
derivative of (2cos(2x-1)/(2cos(x)))	\frac{d}{dx}(\frac{2\cos(2x)-1}{2\cos(x)})
(\partial)/(\partial y)(1+e^xy+xe^xy)	\frac{\partial\:}{\partial\:y}(1+e^{x}y+xe^{x}y)
y^{''}-6y^'+9y=t^{-4}e^{3t}	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=t^{-4}e^{3t}
derivative of f(x)=(2x-8)^5	derivative\:f(x)=(2x-8)^{5}
tangent of 2x^3+4x^2-5x-3	tangent\:2x^{3}+4x^{2}-5x-3
derivative of 2sin(5x)	\frac{d}{dx}(2\sin(5x))
limit as x approaches 0+of 8sqrt(x)ln(x)	\lim\:_{x\to\:0+}(8\sqrt{x}\ln(x))
derivative of F(t)=(3t-1)^4(2t+1)^{-3}	derivative\:F(t)=(3t-1)^{4}(2t+1)^{-3}
ty^'+y=t^4y^3	ty^{\prime\:}+y=t^{4}y^{3}
integral of (ax^2+bx+c)	\int\:(ax^{2}+bx+c)dx
tangent of y=(2x-1)/(x+2)	tangent\:y=\frac{2x-1}{x+2}
derivative of x^2(ln(x))	\frac{d}{dx}(x^{2}(\ln(x)))
derivative of ln(6sec(x))	\frac{d}{dx}(\ln(6\sec(x)))
area f(x)=2x^2-3x+1,1,2	area\:f(x)=2x^{2}-3x+1,1,2
area y=9x,y=x^2	area\:y=9x,y=x^{2}
integral of (sqrt(25x^2-9))/(x^3)	\int\:\frac{\sqrt{25x^{2}-9}}{x^{3}}dx
limit as z approaches 0 of (z^2)/z	\lim\:_{z\to\:0}(\frac{z^{2}}{z})
integral of e^{7x}cos(6x)	\int\:e^{7x}\cos(6x)dx
limit as n approaches infinity of 0.6^n	\lim\:_{n\to\:\infty\:}(0.6^{n})
limit as x approaches 0+of 2+3e^{-3/x}	\lim\:_{x\to\:0+}(2+3e^{-\frac{3}{x}})
inverse oflaplace 1/(x-1)	inverselaplace\:\frac{1}{x-1}
derivative of x^{pi^2}+(pi^2^x)	\frac{d}{dx}(x^{π^{2}}+(π^{2})^{x})
derivative of (sin(2x)/(cos(2x)))	\frac{d}{dx}(\frac{\sin(2x)}{\cos(2x)})
derivative of e^{x-1}-x+1	\frac{d}{dx}(e^{x-1}-x+1)

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