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Popular Calculus Problems
5(dy)/(dt)+y=5t
5\frac{dy}{dt}+y=5t
integral of 30x^3sqrt(1+x^2)
\int\:30x^{3}\sqrt{1+x^{2}}dx
integral of (-4x^2)/(sqrt(4x-x^2))
\int\:\frac{-4x^{2}}{\sqrt{4x-x^{2}}}dx
limit as x approaches 0 of x/(1+x^2)
\lim\:_{x\to\:0}(\frac{x}{1+x^{2}})
f(x)=arcsec(2x)
f(x)=\arcsec(2x)
integral of (sin(6x))^2
\int\:(\sin(6x))^{2}dx
y^'=cos(t)y(1-y/(100))
y^{\prime\:}=\cos(t)y(1-\frac{y}{100})
integral from 0 to 1 of x^2e^{4x}
\int\:_{0}^{1}x^{2}e^{4x}dx
sum from n=1 to infinity of 1/(4^n-3^n)
\sum\:_{n=1}^{\infty\:}\frac{1}{4^{n}-3^{n}}
2(2xy+4y-3)dx+(x+2)^2dy=0
2(2xy+4y-3)dx+(x+2)^{2}dy=0
integral of sin(5x)cos(3x)
\int\:\sin(5x)\cos(3x)dx
sum from n=1 to infinity of (3n)/(n^2+2)
\sum\:_{n=1}^{\infty\:}\frac{3n}{n^{2}+2}
integral from 0 to 2pi of 1
\int\:_{0}^{2π}1
integral from-infinity to 0 of 9^x
\int\:_{-\infty\:}^{0}9^{x}dx
integral of 5m(12m^3-10m)
\int\:5m(12m^{3}-10m)dm
slope of 2x^2+10x-4/(x^2),\at x=-5
slope\:2x^{2}+10x-\frac{4}{x^{2}},\at\:x=-5
x((dy)/(dx))=y+sqrt(x^2-y^2)
x(\frac{dy}{dx})=y+\sqrt{x^{2}-y^{2}}
integral from 0 to 1 of xarcsin(x)
\int\:_{0}^{1}x\arcsin(x)dx
(\partial)/(\partial x)(3xz)
\frac{\partial\:}{\partial\:x}(3xz)
integral of (8e^x)/(e^{2x)-16}
\int\:\frac{8e^{x}}{e^{2x}-16}dx
integral from 0 to pi/2 of sin(2θ)
\int\:_{0}^{\frac{π}{2}}\sin(2θ)dθ
derivative of 3ln(sec(x+tan(x)))
\frac{d}{dx}(3\ln(\sec(x)+\tan(x)))
y^'-e^{x+1}=0
y^{\prime\:}-e^{x+1}=0
integral of sec(x/4)
\int\:\sec(\frac{x}{4})dx
y^{''}+9y=2sin(x)+cos(x)
y^{\prime\:\prime\:}+9y=2\sin(x)+\cos(x)
(dy)/(dx)-xy=x
\frac{dy}{dx}-xy=x
25y^{''}+90y^'+81y=0
25y^{\prime\:\prime\:}+90y^{\prime\:}+81y=0
derivative of 656112^{sqrt(x)}
\frac{d}{dx}(656112^{\sqrt{x}})
integral of 1/(sin(2x))
\int\:\frac{1}{\sin(2x)}dx
derivative of 3sec(8x)
\frac{d}{dx}(3\sec(8x))
derivative of 9excos(x)
derivative\:9ex\cos(x)
integral of (x^4)/(5x^5+4)
\int\:\frac{x^{4}}{5x^{5}+4}dx
derivative of 2e^{2e^x+x}
\frac{d}{dx}(2e^{2e^{x}+x})
integral of 1/(x^2sqrt(x^2-11))
\int\:\frac{1}{x^{2}\sqrt{x^{2}-11}}dx
derivative of e^{(ln(x)/x})
\frac{d}{dx}(e^{\frac{\ln(x)}{x}})
(dy)/(dx)=e^{9x-8y}
\frac{dy}{dx}=e^{9x-8y}
dy+0.15(y-30)dx=0
dy+0.15(y-30)dx=0
derivative of 1/3 x^3-2x^2+3x-4
derivative\:\frac{1}{3}x^{3}-2x^{2}+3x-4
limit as x approaches infinity of 1+8/x
\lim\:_{x\to\:\infty\:}(1+\frac{8}{x})
derivative of 8x^2e^x
derivative\:8x^{2}e^{x}
derivative of sqrt(1-121x^2)arccos(11x)
\frac{d}{dx}(\sqrt{1-121x^{2}}\arccos(11x))
inverse oflaplace s/(s^2+64)
inverselaplace\:\frac{s}{s^{2}+64}
integral of (x^3-4x-6)
\int\:(x^{3}-4x-6)dx
derivative of (3x^2+2(2x-3))
\frac{d}{dx}((3x^{2}+2)(2x-3))
integral of (7x^2)/((9+x^2)^2)
\int\:\frac{7x^{2}}{(9+x^{2})^{2}}dx
integral from 0 to 1 of 16sin^4(x)
\int\:_{0}^{1}16\sin^{4}(x)dx
limit as x approaches 3 of (x-3)/((x-3))
\lim\:_{x\to\:3}(\frac{x-3}{(x-3)})
y^{''}-2y^'+10y=0
y^{\prime\:\prime\:}-2y^{\prime\:}+10y=0
derivative of e^{4/x}
\frac{d}{dx}(e^{\frac{4}{x}})
limit as x approaches 2 of 5x-6
\lim\:_{x\to\:2}(5x-6)
derivative of (4x-8/(x-5))
\frac{d}{dx}(\frac{4x-8}{x-5})
integral of cot(4t)sqrt(1-sin^2(4t))
\int\:\cot(4t)\sqrt{1-\sin^{2}(4t)}dt
integral of (5x^2-5x+14)/((x-2)(x^2+4))
\int\:\frac{5x^{2}-5x+14}{(x-2)(x^{2}+4)}dx
limit as x approaches-3 of x/(x^2-9)
\lim\:_{x\to\:-3}(\frac{x}{x^{2}-9})
integral of 1/2 xe^{2x}
\int\:\frac{1}{2}xe^{2x}dx
derivative of 7^{x^4}
\frac{d}{dx}(7^{x^{4}})
integral of 3cos(x)y+5x^4z^2
\int\:3\cos(x)y+5x^{4}z^{2}dx
integral of e^{x+sin(y)}cos(y)
\int\:e^{x+\sin(y)}\cos(y)dy
derivative of x^2-4x-5
\frac{d}{dx}(x^{2}-4x-5)
sum from n=1 to infinity of 1/(n*(n+1))
\sum\:_{n=1}^{\infty\:}\frac{1}{n\cdot\:(n+1)}
integral of (1+sqrt(x))/(-xsqrt(x))
\int\:\frac{1+\sqrt{x}}{-x\sqrt{x}}dx
integral from 0 to 1 of-(x^2-x)
\int\:_{0}^{1}-(x^{2}-x)dx
limit as x approaches 3 of-sqrt(7-x)
\lim\:_{x\to\:3}(-\sqrt{7-x})
integral of xe^{2x}
\int\:xe^{2x}dx
y^{''''}-4y^{''}=0
y^{\prime\:\prime\:\prime\:\prime\:}-4y^{\prime\:\prime\:}=0
derivative of-(2x^2/(3y^2))
\frac{d}{dx}(-\frac{2x^{2}}{3y^{2}})
integral of-9sin(sqrt(x))
\int\:-9\sin(\sqrt{x})dx
derivative of f(x)=sqrt(x+\sqrt{x)}
derivative\:f(x)=\sqrt{x+\sqrt{x}}
integral of 1/(x-2x^{3/4)-8sqrt(x)}
\int\:\frac{1}{x-2x^{\frac{3}{4}}-8\sqrt{x}}dx
sum from n=0 to infinity of (5+n)/(10^n)
\sum\:_{n=0}^{\infty\:}\frac{5+n}{10^{n}}
integral of ((csc(x)+cot(x))/(sin(x)))
\int\:(\frac{\csc(x)+\cot(x)}{\sin(x)})dx
integral of x^{4035}e^{x^{2018}}
\int\:x^{4035}e^{x^{2018}}dx
limit as x approaches 1 of xarcsin(x/2)
\lim\:_{x\to\:1}(x\arcsin(\frac{x}{2}))
derivative of 3*10^{2x}
\frac{d}{dx}(3\cdot\:10^{2x})
integral of tln(t+1)
\int\:t\ln(t+1)dt
(\partial)/(\partial x)(2(1+y)x)
\frac{\partial\:}{\partial\:x}(2(1+y)x)
derivative of y=3^{x^2+3x}
derivative\:y=3^{x^{2}+3x}
d/(dy)((y^3)/(27)+9/(4y))
\frac{d}{dy}(\frac{y^{3}}{27}+\frac{9}{4y})
derivative of sin(4x)+sin^2(4x)
derivative\:\sin(4x)+\sin^{2}(4x)
f(x)=-3log_{10}(x)
f(x)=-3\log_{10}(x)
f(x)=-2sqrt(x)
f(x)=-2\sqrt{x}
f^'(x)=5x^2+7
f^{\prime\:}(x)=5x^{2}+7
tangent of 4sec(x)-8cos(x)
tangent\:4\sec(x)-8\cos(x)
integral of (sqrt(16x^2+25))/(x^4)
\int\:\frac{\sqrt{16x^{2}+25}}{x^{4}}dx
integral from 0 to pi of cos(2θ)
\int\:_{0}^{π}\cos(2θ)dθ
integral from 0 to 2 of 4x^3-3x^2+2x
\int\:_{0}^{2}4x^{3}-3x^{2}+2xdx
inverse oflaplace ((3s+5))/((s-5)(s+2))
inverselaplace\:\frac{(3s+5)}{(s-5)(s+2)}
integral of (4x)/(sqrt(x^2+9))
\int\:\frac{4x}{\sqrt{x^{2}+9}}dx
derivative of (x^3+1e^x)
\frac{d}{dx}((x^{3}+1)e^{x})
taylor 1/(2x+2)
taylor\:\frac{1}{2x+2}
derivative of (ln(7x)/(7x))
\frac{d}{dx}(\frac{\ln(7x)}{7x})
integral from 0 to infinity of e^{-x}x^2
\int\:_{0}^{\infty\:}e^{-x}x^{2}dx
y^'=0.0016y(2800-y)
y^{\prime\:}=0.0016y(2800-y)
integral of ((x-5))/(x^2-18x+82)
\int\:\frac{(x-5)}{x^{2}-18x+82}dx
derivative of f(x)=1.5x^2+2x^{1.5}
derivative\:f(x)=1.5x^{2}+2x^{1.5}
sum from n=1 to infinity of 1/(n^4+n^2)
\sum\:_{n=1}^{\infty\:}\frac{1}{n^{4}+n^{2}}
derivative of (x^2-3x-4/(x+1))
\frac{d}{dx}(\frac{x^{2}-3x-4}{x+1})
limit as x approaches infinity of 3/(2x)
\lim\:_{x\to\:\infty\:}(\frac{3}{2x})
derivative of sqrt(ax)+a/(sqrt(ax))
\frac{d}{dx}(\sqrt{ax}+\frac{a}{\sqrt{ax}})
derivative of 44(2x^3-5^{6/5})
\frac{d}{dx}(44(2x^{3}-5)^{\frac{6}{5}})
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