-1 / | | x | ----------- dx | _________ | \/ 5 + 4*x | / -2
Integral(x/sqrt(5 + 4*x), (x, -2, -1))
Let .
Then let and substitute :
Integrate term-by-term:
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:
The integral of a constant is the constant times the variable of integration:
The result is:
Now substitute back in:
Now simplify:
Add the constant of integration:
The answer is:
/ | _________ 3/2 | x 5*\/ 5 + 4*x (5 + 4*x) | ----------- dx = C - ------------- + ------------ | _________ 8 24 | \/ 5 + 4*x | /
___ 7 3*I*\/ 3 - -- + --------- 12 4
=
___ 7 3*I*\/ 3 - -- + --------- 12 4
-7/12 + 3*i*sqrt(3)/4
(-0.759777064460204 + 1.21294360408918j)
(-0.759777064460204 + 1.21294360408918j)
Use the examples entering the upper and lower limits of integration.