Question

$\int a^{mx}{b}^{nx}dx$

Answer 1

$\int a^{mx}{b}^{nx}dx$

$\Rightarrow Putting{a}^{mx}{b}^{nx}=t$

$dx[\left(a^{mx}loga\right)b^{nx}+\left(b^{nx}logb\right)a^{nx}]=dt$

or $dx=\frac{dt}{t[loga+logb]}$

$\Rightarrow \int \frac{tdt}{t[loga+logb]}$

$=\frac{t}{[loga+logb]}+c$

$=\frac{a^{mx}{b}^{nx}}{[loga+logb]}+c$