1 / | | 3 | x | ------ dx | 2 | x + 5 | / 0
Integral(x^3/(x^2 + 5), (x, 0, 1))
There are multiple ways to do this integral.
Let .
Then let and substitute :
Rewrite the integrand:
Integrate term-by-term:
The integral of a constant is the constant times the variable of integration:
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of is .
Now substitute back in:
So, the result is:
The result is:
Now substitute back in:
Rewrite the integrand:
Integrate term-by-term:
The integral of is when :
The integral of a constant times a function is the constant times the integral of the function:
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of is .
Now substitute back in:
So, the result is:
So, the result is:
The result is:
Add the constant of integration:
The answer is:
/ | | 3 2 / 2\ | x x 5*log\5 + x / | ------ dx = C + -- - ------------- | 2 2 2 | x + 5 | /
1 5*log(6) 5*log(5) - - -------- + -------- 2 2 2
=
1 5*log(6) 5*log(5) - - -------- + -------- 2 2 2
1/2 - 5*log(6)/2 + 5*log(5)/2
Use the examples entering the upper and lower limits of integration.