Primitive of Reciprocal of Root of a x + b by Root of p x + q/a p greater than 0/Mistake

Source Work

 * $3$: Elementary Analytic Methods
 * $3.3$ Rules for Differentiation and Integration:
 * Integrals of Irrational Algebraic Functions: $3.3.28$

Mistake

 * $\ds \int \frac {\d x} {\sqbrk {\paren {a + b x} \paren {c + d x} }^{1/2} } = \dfrac 2 {\paren {b d}^{1/2} } \ln \size {\sqbrk {b d \paren {a + b x} }^{1/2} + \sqbrk {b \paren {c + d x} }^{1/2} } + C$

Correction
This should read:


 * $\ds \int \frac {\d x} {\sqbrk {\paren {a + b x} \paren {c + d x} }^{1/2} } = \dfrac 2 {\paren {b d}^{1/2} } \ln \size {\sqbrk {d \paren {a + b x} }^{1/2} + \sqbrk {b \paren {c + d x} }^{1/2} } + C$