Mathematics

Integrate the following function: $$\sqrt {ax+b}$$


SOLUTION
$$\int { \sqrt { ax+b }  } dx$$
$$= \int { { \left( ax+b \right)  }^{ \dfrac12 } } dx$$

$$ ={ \dfrac { { \left( ax+b \right)  }^{ \dfrac { 1 }{ 2 } +1 } }{ a } +C } $$

$$=\int { \dfrac { { \left( ax+b \right)  }^{ \dfrac { 3 }{ 2 } } }{ a } +c } .$$

Hence, the answer is $$\int { \dfrac { { \left( ax+b \right)  }^{ \dfrac { 3 }{ 2 } } }{ a } +c } .$$
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Subjective Medium Published on 17th 09, 2020
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