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