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Popular Calculus Problems

derivative of 1/7 pir^3	derivative\:\frac{1}{7}πr^{3}
(\partial)/(\partial x)(ln(3x))	\frac{\partial\:}{\partial\:x}(\ln(3x))
limit as x approaches infinity of 8x^2e^{-x}	\lim\:_{x\to\:\infty\:}(8x^{2}e^{-x})
y^{''}-y^'+y=e^{2t}	y^{\prime\:\prime\:}-y^{\prime\:}+y=e^{2t}
derivative of x(cosh((200/x)-1)-100)	\frac{d}{dx}(x(\cosh(\frac{200}{x})-1)-100)
tangent of f(x)=2x^2+x,\at x=1	tangent\:f(x)=2x^{2}+x,\at\:x=1
derivative of 6/(\sqrt[3]{x^2+5})	\frac{d}{dx}(\frac{6}{\sqrt[3]{x^{2}+5}})
integral of ((ln(x)-1)^2)/x	\int\:\frac{(\ln(x)-1)^{2}}{x}dx
derivative of y= x/3+(3x^2)/2	derivative\:y=\frac{x}{3}+\frac{3x^{2}}{2}
integral from 1 to 32 of (sin(\sqrt[5]{x}))/(\sqrt[5]{x^4)}	\int\:_{1}^{32}\frac{\sin(\sqrt[5]{x})}{\sqrt[5]{x^{4}}}dx
limit as x approaches 0 of ((1))/(x^2)	\lim\:_{x\to\:0}(\frac{(1)}{x^{2}})
integral of ((x^2-x+12))/(x^3+6x)	\int\:\frac{(x^{2}-x+12)}{x^{3}+6x}dx
y^'+2xy=e^x	y^{\prime\:}+2xy=e^{x}
limit as x approaches-6 of x+1	\lim\:_{x\to\:-6}(x+1)
integral of 1/(y^2sqrt(5-y^2))	\int\:\frac{1}{y^{2}\sqrt{5-y^{2}}}dy
integral from 1 to e of 4/z	\int\:_{1}^{e}\frac{4}{z}dz
(d^2)/(dx^2)y+64y=0	\frac{d^{2}}{dx^{2}}y+64y=0
(\partial)/(\partial x)((2y)/(x^2-y^2))	\frac{\partial\:}{\partial\:x}(\frac{2y}{x^{2}-y^{2}})
y^{''}+10y^'+25y=14e^{-5x}	y^{\prime\:\prime\:}+10y^{\prime\:}+25y=14e^{-5x}
limit as x approaches infinity of-1/x	\lim\:_{x\to\:\infty\:}(-\frac{1}{x})
limit as x approaches 1 of cos(pi/3)	\lim\:_{x\to\:1}(\cos(\frac{π}{3}))
derivative of 2/3 pi+1	\frac{d}{dx}(\frac{2}{3}π+1)
integral of cos(4x)cos(5x)	\int\:\cos(4x)\cos(5x)dx
derivative of x^2+6x-3	derivative\:x^{2}+6x-3
49y^{''}+42y^'+9y=0,y(0)=a,y^'(0)=2	49y^{\prime\:\prime\:}+42y^{\prime\:}+9y=0,y(0)=a,y^{\prime\:}(0)=2
area x=((y-3)^2)/3 ,y=9-x	area\:x=\frac{(y-3)^{2}}{3},y=9-x
7sqrt(xy)(dy)/(dx)=2	7\sqrt{xy}\frac{dy}{dx}=2
12=((33000)dy)/(dt)+1/(22*10^{-6)}y	12=\frac{(33000)dy}{dt}+\frac{1}{22\cdot\:10^{-6}}y
limit as h approaches 0 of 3/(sqrt(3h+1)+1)	\lim\:_{h\to\:0}(\frac{3}{\sqrt{3h+1}+1})
derivative of e^{xi}	\frac{d}{dx}(e^{xi})
integral of 3cos^2(x)sin(x)	\int\:3\cos^{2}(x)\sin(x)dx
integral of (2t^2+3)^{4/3}t^3	\int\:(2t^{2}+3)^{\frac{4}{3}}t^{3}dt
derivative of f(x)=(x^2+3x-1)e^x	derivative\:f(x)=(x^{2}+3x-1)e^{x}
limit as n approaches infinity of \|((2n)^{2n})/((2n+2)^{2n)}\|	\lim\:_{n\to\:\infty\:}(\left\|\frac{(2n)^{2n}}{(2n+2)^{2n}}\right\|)
limit as x approaches 2 of 3x-1	\lim\:_{x\to\:2}(3x-1)
sum from n=1 to infinity of 5^nx^n	\sum\:_{n=1}^{\infty\:}5^{n}x^{n}
derivative of arctan(4x)	derivative\:\arctan(4x)
derivative of e^x+sin(x)	\frac{d}{dx}(e^{x}+\sin(x))
integral of u/(sqrt(u))	\int\:\frac{u}{\sqrt{u}}du
(dy)/(dx)+4y=9	\frac{dy}{dx}+4y=9
derivative of (x-2/(9x^2e^x))	\frac{d}{dx}(\frac{x-2}{9x^{2}e^{x}})
area g(x)=x^2,[0,1]	area\:g(x)=x^{2},[0,1]
inverse oflaplace (60)/(2-5s)	inverselaplace\:\frac{60}{2-5s}
derivative of f(x)=x^{5/2}	derivative\:f(x)=x^{\frac{5}{2}}
limit as x approaches-1 of x(x+3)	\lim\:_{x\to\:-1}(x(x+3))
sum from n=0 to infinity of (2/7)^n	\sum\:_{n=0}^{\infty\:}(\frac{2}{7})^{n}
integral from 0 to pi of sin^2(t)	\int\:_{0}^{π}\sin^{2}(t)dt
derivative of ln(3+2x)	\frac{d}{dx}(\ln(3+2x))
limit as x approaches 1 of sqrt(x^2+1)	\lim\:_{x\to\:1}(\sqrt{x^{2}+1})
integral of (cos(x)-sin(x))	\int\:(\cos(x)-\sin(x))dx
integral of cot^6(2x)	\int\:\cot^{6}(2x)dx
integral from 0 to infinity of 1/(x^2+9)	\int\:_{0}^{\infty\:}\frac{1}{x^{2}+9}dx
integral of (x-1)/x	\int\:\frac{x-1}{x}dx
derivative of sin((pix)/3)	derivative\:\sin(\frac{πx}{3})
derivative of f(x)= 3/(2x-4)	derivative\:f(x)=\frac{3}{2x-4}
derivative of e^{2sin(3v)}	derivative\:e^{2\sin(3v)}
derivative of xy+ln(x/y)	\frac{d}{dx}(xy+\ln(\frac{x}{y}))
y^{''}-6y^'+9y=0,y(0)=2,y^'(0)= 25/3	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=0,y(0)=2,y^{\prime\:}(0)=\frac{25}{3}
integral of 2y-5	\int\:2y-5dy
derivative of ((4x^2+8x+4))/(sqrt(x))	derivative\:\frac{(4x^{2}+8x+4)}{\sqrt{x}}
integral of sin(8pit)	\int\:\sin(8πt)dt
xy^'=y+2sqrt(xy)	xy^{\prime\:}=y+2\sqrt{xy}
derivative of arctan(16x)	derivative\:\arctan(16x)
integral of arcsec(4x)	\int\:\arcsec(4x)dx
integral of sqrt(y)-y	\int\:\sqrt{y}-ydy
derivative of (13)/(ln(x))	derivative\:\frac{13}{\ln(x)}
derivative of sin(9ln(x))	derivative\:\sin(9\ln(x))
integral of 1/(sqrt(441-x^2))	\int\:\frac{1}{\sqrt{441-x^{2}}}dx
derivative of cos(x+x)	\frac{d}{dx}(\cos(x)+x)
derivative of 3x^2-12x	\frac{d}{dx}(3x^{2}-12x)
integral of ln(12x)	\int\:\ln(12x)dx
integral of 2xe^{x^2+3}	\int\:2xe^{x^{2}+3}dx
limit as x approaches 8 of (x-8)/(x^{1/3)-2}	\lim\:_{x\to\:8}(\frac{x-8}{x^{\frac{1}{3}}-2})
limit as x approaches+0 of (3x)/(xe^x)	\lim\:_{x\to\:+0}(\frac{3x}{xe^{x}})
derivative of arcsin(9x^4)	\frac{d}{dx}(\arcsin(9x^{4}))
d/(d{y)}((6{x}+{y})/(8{z)-5{y}})	\frac{d}{d{y}}(\frac{6{x}+{y}}{8{z}-5{y}})
derivative of-4ln(x)	\frac{d}{dx}(-4\ln(x))
(4x^3+3x^2+3y-1)dx+(3x+2y+1)dy=0	(4x^{3}+3x^{2}+3y-1)dx+(3x+2y+1)dy=0
limit as x approaches infinity of (5e^{-3x}+2)/(e^{-5x)+4}	\lim\:_{x\to\:\infty\:}(\frac{5e^{-3x}+2}{e^{-5x}+4})
integral of (5x+3)\sqrt[3]{5x^2+6x}	\int\:(5x+3)\sqrt[3]{5x^{2}+6x}dx
y^{''}+7y^'+10y=4te^{4t}	y^{\prime\:\prime\:}+7y^{\prime\:}+10y=4te^{4t}
sum from n=1 to infinity of (cos(1.4))^n	\sum\:_{n=1}^{\infty\:}(\cos(1.4))^{n}
integral from 0 to t of t^2e^{-5t}	\int\:_{0}^{t}t^{2}e^{-5t}dt
d/(dt)(e^{-6t})	\frac{d}{dt}(e^{-6t})
y^'-6+y/((4(x+250)))=0,y(0)=70	y^{\prime\:}-6+\frac{y}{(4(x+250))}=0,y(0)=70
integral from 0 to 1/2 of arcsin(2y)	\int\:_{0}^{\frac{1}{2}}\arcsin(2y)dy
derivative of xln(x-1)	\frac{d}{dx}(x\ln(x)-1)
derivative of x/(arctan(x))	\frac{d}{dx}(\frac{x}{\arctan(x)})
implicit (dy)/(dx),ysin(1/y)=1-xy	implicit\:\frac{dy}{dx},y\sin(\frac{1}{y})=1-xy
derivative of log_{8}(sqrt(x))	\frac{d}{dx}(\log_{8}(\sqrt{x}))
integral of 7e^{-0.5x}	\int\:7e^{-0.5x}dx
7y^{''}+13y^'-2y=0	7y^{\prime\:\prime\:}+13y^{\prime\:}-2y=0
simplify 2t^{-1/4}	simplify\:2t^{-\frac{1}{4}}
integral from 0 to pi of cos^4(2x)	\int\:_{0}^{π}\cos^{4}(2x)dx
derivative of 8x^3-2x	\frac{d}{dx}(8x^{3}-2x)
limit as x approaches+1000 of 18pi^2	\lim\:_{x\to\:+1000}(18π^{2})
derivative of arccsc(3x)	\frac{d}{dx}(\arccsc(3x))
integral of (tan(5x)+csc^3(3θ))	\int\:(\tan(5x)+\csc^{3}(3θ))dθ
integral of (sec^2(x)+1)	\int\:(\sec^{2}(x)+1)dx
laplacetransform F(x)=e^{2x}cos(2x)	laplacetransform\:F(x)=e^{2x}\cos(2x)

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