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