1 / | | _________ | \/ 3*x + 5 dx | / 0
Integral(sqrt(3*x + 5), (x, 0, 1))
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is when :
So, the result is:
Now substitute back in:
Now simplify:
Add the constant of integration:
The answer is:
/ | 3/2 | _________ 2*(3*x + 5) | \/ 3*x + 5 dx = C + -------------- | 9 /
___ ___ 10*\/ 5 32*\/ 2 - -------- + -------- 9 9
=
___ ___ 10*\/ 5 32*\/ 2 - -------- + -------- 9 9
-10*sqrt(5)/9 + 32*sqrt(2)/9
Use the examples entering the upper and lower limits of integration.