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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
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Integral of x^(-1/2)
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Integral of 1/sqrt(1+u^2)
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Integral of -e^x
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Integral of (2x+3)
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Identical expressions
- one /(pi*((x^ two)+ four *x+ five))
- 1 divide by ( Pi multiply by ((x squared ) plus 4 multiply by x plus 5))
- one divide by ( Pi multiply by ((x to the power of two) plus four multiply by x plus five))
- 1/(pi*((x2)+4*x+5))
- 1/pi*x2+4*x+5
- 1/(pi*((x²)+4*x+5))
- 1/(pi*((x to the power of 2)+4*x+5))
- 1/(pi((x^2)+4x+5))
- 1/(pi((x2)+4x+5))
- 1/pix2+4x+5
- 1/pix^2+4x+5
- 1 divide by (pi*((x^2)+4*x+5))
- 1/(pi*((x^2)+4*x+5))dx
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Similar expressions
- 1/(pi*((x^2)+4*x-5))
- 1/(pi*((x^2)-4*x+5))
Integral of 1/(pi*((x^2)+4*x+5)) dx
The solution
You have entered
[src]
oo / | | 1 | ----------------- dx | / 2 \ | pi*\x + 4*x + 5/ | / -1
$$\int\limits_{-1}^{\infty} \frac{1}{\pi \left(\left(x^{2} + 4 x\right) + 5\right)}\, dx$$
Integral(1/(pi*(x^2 + 4*x + 5)), (x, -1, oo))
Detail solution
We have the integral:
/ | | 1 | ----------------- dx | / 2 \ | pi*\x + 4*x + 5/ | /
Rewrite the integrand
/ 1 \
|----|
1 \pi*1/
----------------- = -------------
/ 2 \ 2
pi*\x + 4*x + 5/ (-x - 2) + 1or
/ | | 1 | ----------------- dx | / 2 \ = | pi*\x + 4*x + 5/ | /
/
|
| 1
| ------------- dx
| 2
| (-x - 2) + 1
|
/
-------------------
pi In the integral
/
|
| 1
| ------------- dx
| 2
| (-x - 2) + 1
|
/
-------------------
pi do replacement
v = -2 - x
then
the integral =
/
|
| 1
| ------ dv
| 2
| 1 + v
|
/ atan(v)
------------ = -------
pi pi do backward replacement
/
|
| 1
| ------------- dx
| 2
| (-x - 2) + 1
|
/ atan(2 + x)
------------------- = -----------
pi pi Solution is:
atan(2 + x)
C + -----------
pi
The answer (Indefinite)
[src]
/ | | 1 atan(2 + x) | ----------------- dx = C + ----------- | / 2 \ pi | pi*\x + 4*x + 5/ | /
$$\int \frac{1}{\pi \left(\left(x^{2} + 4 x\right) + 5\right)}\, dx = C + \frac{\operatorname{atan}{\left(x + 2 \right)}}{\pi}$$
The graph
Use the examples entering the upper and lower limits of integration.