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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x/(1-x^2)^1/2
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Integral of x^2*e^(4*x)
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Integral of x*(-2)/(1+x^2)
- Integral of x^2√(1-x^2)
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Identical expressions
- arctg(x/(x+ one))
- arctg(x divide by (x plus 1))
- arctg(x divide by (x plus one))
- arctgx/x+1
- arctg(x divide by (x+1))
- arctg(x/(x+1))dx
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Similar expressions
- arctg(x/(x-1))
Integral of arctg(x/(x+1)) dx
The solution
You have entered
[src]
oo / | | / x \ | atan|-----| dx | \x + 1/ | / 1
$$\int\limits_{1}^{\infty} \operatorname{atan}{\left(\frac{x}{x + 1} \right)}\, dx$$
Integral(atan(x/(x + 1)), (x, 1, oo))
The answer (Indefinite)
[src]
/ | / 2\ | / x \ atan(1 + 2*x) log\1 + 2*x + 2*x / / x \ | atan|-----| dx = C + ------------- - ------------------- + x*atan|-----| | \x + 1/ 2 4 \x + 1/ | /
$$\int \operatorname{atan}{\left(\frac{x}{x + 1} \right)}\, dx = C + x \operatorname{atan}{\left(\frac{x}{x + 1} \right)} - \frac{\log{\left(2 x^{2} + 2 x + 1 \right)}}{4} + \frac{\operatorname{atan}{\left(2 x + 1 \right)}}{2}$$
The graph
Use the examples entering the upper and lower limits of integration.