4
dx, v = x. Then
4x + 1
R 4x
R (4x + 1) − 1
dx = x ln(4x + 1) −
dx
= x ln(4x + 1) −
4x
+
1
4x
+
1
R
1
dx
= x ln(4x + 1) −
1−
4x + 1
= x ln(4x + 1) − x + 41 ln(4x + 1) + C
= 14 (4x + 1) ln(4x + 1) − x + C.
Let u = ln(4x + 1), dv = dx ⇒ du =
R
ln(4x + 1) dx