Question

integrate of 5dx / √x+3 - √x-2​

Answer 1

Let I=∫x51+x3−−−−−√dx

Assume 1+x3=y2

⟹3x2dx=2ydy

Substitution of x , gives us,

=∫2(y2−1)y3ydx

=∫2(y2−1)3dx

=2y39−2y3

Substitution of y, gives us,

I=2(1+x3−−−−−√)39−21+x3−−−−−√3+C (where C is the arbitrary constant of indefinite integration)

if there is a problem then I'm sorry please