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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^(x/2)
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Integral of e^(3*x)*dx
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Integral of x^2*exp(x^3)
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Integral of dy/y^2
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Identical expressions
- arctg(x/(x+ two))
- arctg(x divide by (x plus 2))
- arctg(x divide by (x plus two))
- arctgx/x+2
- arctg(x divide by (x+2))
- arctg(x/(x+2))dx
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Similar expressions
- arctg(x/(x-2))
- x^5*arctgx/((x+2)^2(x+4)^0,5)
Integral of arctg(x/(x+2)) dx
The solution
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[src]
oo / | | / x \ | atan|-----| dx | \x + 2/ | / 1
$$\int\limits_{1}^{\infty} \operatorname{atan}{\left(\frac{x}{x + 2} \right)}\, dx$$
Integral(atan(x/(x + 2)), (x, 1, oo))
The answer (Indefinite)
[src]
/ | / 2 \ | / x \ log\2 + x + 2*x/ / x \ | atan|-----| dx = C - ----------------- + x*atan|-----| + atan(1 + x) | \x + 2/ 2 \x + 2/ | /
$$\int \operatorname{atan}{\left(\frac{x}{x + 2} \right)}\, dx = C + x \operatorname{atan}{\left(\frac{x}{x + 2} \right)} - \frac{\log{\left(x^{2} + 2 x + 2 \right)}}{2} + \operatorname{atan}{\left(x + 1 \right)}$$
The graph
Use the examples entering the upper and lower limits of integration.