Question

evaluate the integral

Answer 1

\[\int\limits_{?}^{?} \frac{ 3x dx }{\sqrt{4x^2+5} }\]

Answer 2

u=4x^2+5.

Answer 3

du=8x dx

Answer 4

and...?

Answer 5

rewrite the integral in terms of u and du.

integral(3x dx/sqrt(4x^2+5))=integral(3x dx/sqrt(u)).

since du=8x dx, dx=du/8x.

integral(3x dx/sqrt(u))=integral(3/(8*sqrt(u)) du)=3sqrt(u)/4=3sqrt(4x^2+5)/4