Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of x/(x^2+2x+2)
-
Integral of x(x^2+3)dx
-
Integral of x*cos(x^3)
-
Integral of x/(5-3x^2)
-
Identical expressions
- x/(five -3x^ two)
- x divide by (5 minus 3x squared )
- x divide by (five minus 3x to the power of two)
- x/(5-3x2)
- x/5-3x2
- x/(5-3x²)
- x/(5-3x to the power of 2)
- x/5-3x^2
- x divide by (5-3x^2)
- x/(5-3x^2)dx
-
Similar expressions
- x/(5+3x^2)
Integral of x/(5-3x^2) dx
The solution
You have entered
[src]
1 / | | x | -------- dx | 2 | 5 - 3*x | / 0
$$\int\limits_{0}^{1} \frac{x}{5 - 3 x^{2}}\, dx$$
Integral(x/(5 - 3*x^2), (x, 0, 1))
Detail solution
We have the integral:
/ | | x | -------- dx | 2 | 5 - 3*x | /
Rewrite the integrand
-3*2*x
- ----------------
2
x - 3*x + 0*x + 5
-------- = -------------------
2 6
5 - 3*x or
/ | | x | -------- dx | 2 = | 5 - 3*x | /
/
|
| -3*2*x
- | ---------------- dx
| 2
| - 3*x + 0*x + 5
|
/
------------------------
6 In the integral
/
|
| -3*2*x
- | ---------------- 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
- | ---------------- dx
| 2
| - 3*x + 0*x + 5
| / 2\
/ -log\-5 + 3*x /
------------------------ = ----------------
6 6 Solution is:
/ 2\
log\-5 + 3*x /
C - --------------
6
The answer (Indefinite)
[src]
/ | / 2\ | x log\5 - 3*x / | -------- dx = C - ------------- | 2 6 | 5 - 3*x | /
$$\int \frac{x}{5 - 3 x^{2}}\, dx = C - \frac{\log{\left(5 - 3 x^{2} \right)}}{6}$$
The graph
The answer
[src]
log(2) log(5)
- ------ + ------
6 6
$$- \frac{\log{\left(2 \right)}}{6} + \frac{\log{\left(5 \right)}}{6}$$
=
=
log(2) log(5)
- ------ + ------
6 6
$$- \frac{\log{\left(2 \right)}}{6} + \frac{\log{\left(5 \right)}}{6}$$
-log(2)/6 + log(5)/6
The graph
Use the examples entering the upper and lower limits of integration.