Question

pls give me detailed solution of this question​

Answer 1

$\pink{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: \: \: given \\ \\ \displaystyle \int \bf \: \frac{3ax}{ {b}^{2} + {c}^{2} {x}^{2} } \: dx \\ \\ \blue{{\boxed{\begin{array}{cc} \bf \: substitute \: \: \\ \bf \: u = {b}^{2} + {c}^{2} {x}^{2} \\ \bf \implies \: \frac{du}{dx} =0+ 2 {c}^{2} x \\ \bf \implies \: dx = \frac{1}{2 {c}^{2} x} du \: \end{array}}}} \\ \\ = \bf \frac{3a}{2 {c}^{2} } \displaystyle \int \bf \: \frac{1}{u} \: du \\ \\ = \bf \frac{3a}{2 {c}^{2} } \times \ln(u) + c\: \\ \\ = \bf \: \frac{3a}{2 {c}^{2} } \times \ln( {b}^{2} + {c}^{2} {x}^{2} ) + c \end{array}}}}$

Note :

$\bf \odot \: \displaystyle \int \bf \: \frac{1}{x} \: dx = \ln(x) + c$