Mathematics

Solve :
$$ \int (3x+5)^7 dx $$


SOLUTION
$$\begin{array}{l} \int _{  }^{  }{ { { \left( { 3x+5 } \right)  }^{ 7 } } } dx \\ Put\, \, \left( { 3x+5 } \right) =t\, so\, that\, \, 3dx\, =dt\, or\, dx=\frac { 1 }{ 3 } dt. \\ \therefore \int _{  }^{  }{ { { \left( { 3x+5 } \right)  }^{ 7 } } } dx \\ =\frac { 1 }{ 3 } .\frac { { { t^{ 8 } } } }{ 8 } +C \\ =\frac { { { { \left( { 3x+5 } \right)  }^{ 8 } } } }{ { 24 } } +C \end{array}$$
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Subjective Medium Published on 17th 09, 2020
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