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How to use it?
- Integral of d{x}:
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Integral of t+1
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Integral of 2*x/(x-1)
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Integral of 1/(sqrt(4-9x^2))
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Integral of tg^2*x*dx
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Identical expressions
- one /((9x^ two)+ one)
- 1 divide by ((9x squared ) plus 1)
- one divide by ((9x to the power of two) plus one)
- 1/((9x2)+1)
- 1/9x2+1
- 1/((9x²)+1)
- 1/((9x to the power of 2)+1)
- 1/9x^2+1
- 1 divide by ((9x^2)+1)
- 1/((9x^2)+1)dx
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Similar expressions
- 1/((9x^2)-1)
Integral of 1/((9x^2)+1) dx
The solution
You have entered
[src]
oo / | | 1 | -------- dx | 2 | 9*x + 1 | / 0
$$\int\limits_{0}^{\infty} \frac{1}{9 x^{2} + 1}\, dx$$
Integral(1/(9*x^2 + 1), (x, 0, oo))
Detail solution
We have the integral:
/ | | 1 | -------- dx | 2 | 9*x + 1 | /
Rewrite the integrand
1 1 -------- = --------------- 2 / 2 \ 9*x + 1 1*\(-3*x) + 1/
or
/ | | 1 | -------- dx | 2 = | 9*x + 1 | /
/ | | 1 | ----------- dx | 2 | (-3*x) + 1 | /
In the integral
/ | | 1 | ----------- dx | 2 | (-3*x) + 1 | /
do replacement
v = -3*x
then
the integral =
/ | | 1 | ------ dv = atan(v) | 2 | 1 + v | /
do backward replacement
/ | | 1 atan(3*x) | ----------- dx = --------- | 2 3 | (-3*x) + 1 | /
Solution is:
atan(3*x)
C + ---------
3
The answer (Indefinite)
[src]
/ | | 1 atan(3*x) | -------- dx = C + --------- | 2 3 | 9*x + 1 | /
$$\int \frac{1}{9 x^{2} + 1}\, dx = C + \frac{\operatorname{atan}{\left(3 x \right)}}{3}$$
The graph
Use the examples entering the upper and lower limits of integration.