4 / | | 2*x | -------------- dx | 2 | ___ ___ | \/ x + \/ 8 | / 2
Integral((2*x)/((sqrt(x))^2 + sqrt(8)), (x, 2, 4))
There are multiple ways to do this integral.
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
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:
So, the result is:
Now substitute back in:
Rewrite the integrand:
The integral of a constant times a function is the constant times the integral of the function:
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:
So, the result is:
Rewrite the integrand:
The integral of a constant times a function is the constant times the integral of the function:
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:
So, the result is:
Add the constant of integration:
The answer is:
/ | | 2*x ___ / ___\ | -------------- dx = C + 2*x - 4*\/ 2 *log\x + 2*\/ 2 / | 2 | ___ ___ | \/ x + \/ 8 | /
___ / ___\ ___ / ___\ 4 - 4*\/ 2 *log\4 + 2*\/ 2 / + 4*\/ 2 *log\2 + 2*\/ 2 /
=
___ / ___\ ___ / ___\ 4 - 4*\/ 2 *log\4 + 2*\/ 2 / + 4*\/ 2 *log\2 + 2*\/ 2 /
4 - 4*sqrt(2)*log(4 + 2*sqrt(2)) + 4*sqrt(2)*log(2 + 2*sqrt(2))
Use the examples entering the upper and lower limits of integration.