MATHEMATICS II

Taking derivatives of both sides we get:

du=(2x+3)dx

Thus:

(4x+6)dx=2(2x+3)dx=2du; (since du=(2x+3)dx)

So we can rewrite the ingegral expression as:

Taking derivatives of both sides, we get:

du=2xdx

(1/2)du=xdx

Thus we now can transform our integral to the one in the form of:

Taking derivatives of both sides we get:

du=0.5*2*(2x+6)^-0.5dx

du=(2x+6)^-0.5dx

Then our integral can be rewritten as:

du=(1/x)dx and (1/3)x³=v.

So we get:

Thus, the answer is D.

Thus, the answer is D.

Thus, the answer is B.

The answer is E.