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