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How to use it?
- Integral of d{x}:
-
Integral of (4x-x^2)dx
-
Integral of (2x+3)/(x^2-5x+6)
- Integral of xcoskx
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Integral of -xe^x
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Identical expressions
- x/(3x^ two + five)
- x divide by (3x squared plus 5)
- x divide by (3x to the power of two plus five)
- x/(3x2+5)
- x/3x2+5
- x/(3x²+5)
- x/(3x to the power of 2+5)
- x/3x^2+5
- x divide by (3x^2+5)
- x/(3x^2+5)dx
-
Similar expressions
- x*dx/(3*x^2+5)
- x/(3x^2-5)
Integral of x/(3x^2+5) dx
The solution
You have entered
[src]
1 / | | x | -------- dx | 2 | 3*x + 5 | / 0
$$\int\limits_{0}^{1} \frac{x}{3 x^{2} + 5}\, dx$$
Integral(x/(3*x^2 + 5), (x, 0, 1))
Detail solution
We have the integral:
/ | | x | 1*-------- dx | 2 | 3*x + 5 | /
Rewrite the integrand
/ 3*2*x + 0 \
|--------------| /0\
| 2 | |-|
x \3*x + 0*x + 5/ \5/
-------- = ---------------- + ---------------------
2 6 2
3*x + 5 / ____ \
|-\/ 15 |
|--------*x + 0| + 1
\ 5 / or
/ | | x | 1*-------- dx | 2 = | 3*x + 5 | /
/
|
| 3*2*x + 0
| -------------- dx
| 2
| 3*x + 0*x + 5
|
/
--------------------
6 In the integral
/
|
| 3*2*x + 0
| -------------- dx
| 2
| 3*x + 0*x + 5
|
/
--------------------
6 do replacement
2 u = 3*x
then
the integral =
/
|
| 1
| ----- du
| 5 + u
|
/ log(5 + u)
----------- = ----------
6 6 do backward replacement
/
|
| 3*2*x + 0
| -------------- dx
| 2
| 3*x + 0*x + 5
| / 2\
/ log\5 + 3*x /
-------------------- = -------------
6 6 In the integral
0
do replacement
____
-x*\/ 15
v = ----------
5 then
the integral =
0 = 0
do backward replacement
0 = 0
Solution is:
/ 2\
log\5 + 3*x /
C + -------------
6
The answer (Indefinite)
[src]
/ | / 2\ | x log\5 + 3*x / | -------- dx = C + ------------- | 2 6 | 3*x + 5 | /
$${{\log \left(3\,x^2+5\right)}\over{6}}$$
The graph
The answer
[src]
log(5) log(8)
- ------ + ------
6 6
$${{\log 8}\over{6}}-{{\log 5}\over{6}}$$
=
=
log(5) log(8)
- ------ + ------
6 6
$$- \frac{\log{\left(5 \right)}}{6} + \frac{\log{\left(8 \right)}}{6}$$
The graph
Use the examples entering the upper and lower limits of integration.