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How to use it?
- Integral of d{x}:
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Integral of s
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Integral of sec^3(x)
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Integral of e^y
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Integral of x/(1+x)
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Identical expressions
- dz/(z^ two + one)
- dz divide by (z squared plus 1)
- dz divide by (z to the power of two plus one)
- dz/(z2+1)
- dz/z2+1
- dz/(z²+1)
- dz/(z to the power of 2+1)
- dz/z^2+1
- dz divide by (z^2+1)
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Similar expressions
- dz/(z^2-1)
Integral of dz/(z^2+1) dx
The solution
You have entered
[src]
1 / | | 1 | ------ dz | 2 | z + 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{z^{2} + 1}\, dz$$
Integral(1/(z^2 + 1), (z, 0, 1))
Detail solution
We have the integral:
/ | | 1 | ------ dz | 2 | z + 1 | /
Rewrite the integrand
1 1 ------ = ------------- 2 / 2 \ z + 1 1*\(-z) + 1/
or
/ | | 1 | ------ dz | 2 = | z + 1 | /
/ | | 1 | --------- dz | 2 | (-z) + 1 | /
In the integral
/ | | 1 | --------- dz | 2 | (-z) + 1 | /
do replacement
v = -z
then
the integral =
/ | | 1 | ------ dv = atan(v) | 2 | 1 + v | /
do backward replacement
/ | | 1 | --------- dz = atan(z) | 2 | (-z) + 1 | /
Solution is:
C + atan(z)
The answer (Indefinite)
[src]
/ | | 1 | ------ dz = C + atan(z) | 2 | z + 1 | /
$$\int \frac{1}{z^{2} + 1}\, dz = C + \operatorname{atan}{\left(z \right)}$$
The graph
Use the examples entering the upper and lower limits of integration.