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- Improper integral
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How to use it?
- Integral of d{x}:
-
Integral of sinx
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Integral of sin(x²)
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Integral of x^2/sqrt(1+x^4)
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Integral of (x^2+2x)/(x+1)
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Identical expressions
- dx/(sixteen +16x^ two)
- dx divide by (16 plus 16x squared )
- dx divide by (sixteen plus 16x to the power of two)
- dx/(16+16x2)
- dx/16+16x2
- dx/(16+16x²)
- dx/(16+16x to the power of 2)
- dx/16+16x^2
- dx divide by (16+16x^2)
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Similar expressions
- dx/(16-16x^2)
Integral of dx/(16+16x^2) dx
The solution
You have entered
[src]
0 / | | 1 | ---------- dx | 2 | 16 + 16*x | / -oo
$$\int\limits_{-\infty}^{0} \frac{1}{16 x^{2} + 16}\, dx$$
Integral(1/(16 + 16*x^2), (x, -oo, 0))
Detail solution
We have the integral:
/ | | 1 | ---------- dx | 2 | 16 + 16*x | /
Rewrite the integrand
1 1
---------- = --------------
2 / 2 \
16 + 16*x 16*\(-x) + 1/or
/ | | 1 | ---------- dx | 2 = | 16 + 16*x | /
/
|
| 1
| --------- dx
| 2
| (-x) + 1
|
/
---------------
16 In the integral
/
|
| 1
| --------- dx
| 2
| (-x) + 1
|
/
---------------
16 do replacement
v = -x
then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
16 16 do backward replacement
/
|
| 1
| --------- dx
| 2
| (-x) + 1
|
/ atan(x)
--------------- = -------
16 16 Solution is:
atan(x)
C + -------
16
The answer (Indefinite)
[src]
/ | | 1 atan(x) | ---------- dx = C + ------- | 2 16 | 16 + 16*x | /
$$\int \frac{1}{16 x^{2} + 16}\, dx = C + \frac{\operatorname{atan}{\left(x \right)}}{16}$$
The graph
Use the examples entering the upper and lower limits of integration.