Question

1
If уз
then y dx will be:
ax + b
(1)
+C
(2) ax + b + c
(ax + b)2
In(ax +b)
+
+C
(4)
(3) aln(ax+b)+C
a
1​

Answer 1

Let ax + b = t

=> a = dt/dx

=> dx = dt/a

Substitute the value of dx in

$\int \frac{1}{ax + b} dx$

we get,

$\int \frac{dt}{at}$

$= \frac{1}{a} \int \frac{dt}{t}$

$= \frac{1}{a} log(t) + c$

substitute the value of t in above expression

$\frac{1}{a} log(ax + b) + c$

Thus, correct option : 4) [ln(ax+b)]/a + c