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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of e^3x
- Integral of sinx/cos2x
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Integral of -e^x
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Integral of sqrt(x^2+1)/x^3
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Identical expressions
- x*arcctg(x/ five)
- x multiply by arcctg(x divide by 5)
- x multiply by arcctg(x divide by five)
- xarcctg(x/5)
- xarcctgx/5
- x*arcctg(x divide by 5)
- x*arcctg(x/5)dx
Integral of x*arcctg(x/5) dx
The solution
You have entered
[src]
1 / | | /x\ | x*acot|-| dx | \5/ | / 0
$$\int\limits_{0}^{1} x \operatorname{acot}{\left(\frac{x}{5} \right)}\, dx$$
Integral(x*acot(x/5), (x, 0, 1))
The answer (Indefinite)
[src]
/ /x\ 2 /x\ | 25*acot|-| x *acot|-| | /x\ 5*x \5/ \5/ | x*acot|-| dx = C + --- + ---------- + ---------- | \5/ 2 2 2 | /
$$\int x \operatorname{acot}{\left(\frac{x}{5} \right)}\, dx = C + \frac{x^{2} \operatorname{acot}{\left(\frac{x}{5} \right)}}{2} + \frac{5 x}{2} + \frac{25 \operatorname{acot}{\left(\frac{x}{5} \right)}}{2}$$
The graph
The answer
[src]
5 25*pi - + 13*acot(1/5) - ----- 2 4
$$- \frac{25 \pi}{4} + \frac{5}{2} + 13 \operatorname{acot}{\left(\frac{1}{5} \right)}$$
=
=
5 25*pi - + 13*acot(1/5) - ----- 2 4
$$- \frac{25 \pi}{4} + \frac{5}{2} + 13 \operatorname{acot}{\left(\frac{1}{5} \right)}$$
5/2 + 13*acot(1/5) - 25*pi/4
Use the examples entering the upper and lower limits of integration.