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How to use it?
- Integral of d{x}:
-
Integral of 1/(2+x^2)
- Integral of (x^2+cos(x^2))/(sqrt(8x-x^4))
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Integral of sin³xcosx
- Integral of (ln(1+x))/(1+x^2)
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Identical expressions
- (x+ two)/(x²+4x+ eight)
- (x plus 2) divide by (x² plus 4x plus 8)
- (x plus two) divide by (x² plus 4x plus eight)
- x+2/x²+4x+8
- (x+2) divide by (x²+4x+8)
- (x+2)/(x²+4x+8)dx
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Similar expressions
- (x-2)/(x²+4x+8)
- (x+2)/(x²+4x-8)
- (x+2)/(x²-4x+8)
Integral of (x+2)/(x²+4x+8) dx
The solution
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[src]
1 / | | x + 2 | ------------ dx | 2 | x + 4*x + 8 | / 0
$$\int\limits_{0}^{1} \frac{x + 2}{\left(x^{2} + 4 x\right) + 8}\, dx$$
Integral((x + 2)/(x^2 + 4*x + 8), (x, 0, 1))
Detail solution
We have the integral:
/ | | x + 2 | ------------ dx | 2 | x + 4*x + 8 | /
Rewrite the integrand
/ 2*x + 4 \
|------------| /0\
| 2 | |-|
x + 2 \x + 4*x + 8/ \4/
------------ = -------------- + --------------
2 2 2
x + 4*x + 8 / x \
|- - - 1| + 1
\ 2 / or
/ | | x + 2 | ------------ dx | 2 = | x + 4*x + 8 | /
/
|
| 2*x + 4
| ------------ dx
| 2
| x + 4*x + 8
|
/
------------------
2 In the integral
/
|
| 2*x + 4
| ------------ dx
| 2
| x + 4*x + 8
|
/
------------------
2 do replacement
2 u = x + 4*x
then
the integral =
/
|
| 1
| ----- du
| 8 + u
|
/ log(8 + u)
----------- = ----------
2 2 do backward replacement
/
|
| 2*x + 4
| ------------ dx
| 2
| x + 4*x + 8
| / 2 \
/ log\8 + x + 4*x/
------------------ = -----------------
2 2 In the integral
0
do replacement
x
v = -1 - -
2then
the integral =
True
do backward replacement
True
Solution is:
/ 2 \
log\8 + x + 4*x/
C + -----------------
2
The answer (Indefinite)
[src]
/ | / 2 \ | x + 2 log\x + 4*x + 8/ | ------------ dx = C + ----------------- | 2 2 | x + 4*x + 8 | /
$$\int \frac{x + 2}{\left(x^{2} + 4 x\right) + 8}\, dx = C + \frac{\log{\left(\left(x^{2} + 4 x\right) + 8 \right)}}{2}$$
The graph
The answer
[src]
log(13) log(8) ------- - ------ 2 2
$$- \frac{\log{\left(8 \right)}}{2} + \frac{\log{\left(13 \right)}}{2}$$
=
=
log(13) log(8) ------- - ------ 2 2
$$- \frac{\log{\left(8 \right)}}{2} + \frac{\log{\left(13 \right)}}{2}$$
log(13)/2 - log(8)/2
Use the examples entering the upper and lower limits of integration.