i need some help please?

Question

i have 3 problems that are integrated by parts for some reason im not getting them.

1) int x arctan(2x) dx

2) int x sin^2(4x) dx

3) int ln(x^2+9x+14) dx

Answer 1

Here are the answers you should get:

1) 1/8((4x^2 +1) arctan(2x) -2x) + C

2) x^2/4 - x sin(8x)/16 - cos(8x)/128 + C

3) ln(x^2+9x+14)x -2x +2ln(x+2) + 7ln(x+7) + C

For 3, use the following: x^2+9x+14 = (x+2)(x+7) and ln(ab) = ln(a)+ln(b) and Integral ln(x) dx = x(ln(x)-1).

Answer 2

The first one is (1/2)*(x² + (1/4))*arctan(2x) - (x/4)

Just keep dicking around with it until you get the right v and du ☺


Doug