Mathematics

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

##### SOLUTION
$\int { { a }^{ mx } } { b }^{ nx }dx$
$\Rightarrow \quad Putting\quad { a }^{ mx }{ b }^{ nx }=t$
$dx\left[ \left( { a }^{ mx }loga \right) { b }^{ nx }+\left( { b }^{ nx }logb \right) { a }^{ nx } \right] =dt$
or    $dx=\dfrac { dt }{ t\left[ loga+logb \right] }$
$\Rightarrow \int { \dfrac { tdt }{ t\left[ loga+logb \right] } }$
$=\dfrac { t }{ \left[ loga+logb \right] } +c$
$=\dfrac { { a }^{ mx }{ b }^{ nx } }{ \left[ loga+logb \right] } +c$

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Subjective Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

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