Mathematics

Solve $$\displaystyle\int { \dfrac { x }{ \sqrt { x+4 }  } dx }$$


SOLUTION
$$\begin{array}{l} \int { \dfrac { x }{ { \sqrt { x+4 }  } } dx }  \\ putting\, x+4={ t^{ 2 } } \\ dx=2tdt \\ =\int { \dfrac { { { t^{ 2 } }-4 } }{ t }  } \times 2tdt \\ =2\int { \left( { { t^{ 2 } }-4 } \right)  } dt \\ =2\left[ { \dfrac { { { t^{ 3 } } } }{ 3 } -4t } \right] +c \\ =2\left[ { \dfrac { { { { \left( { x+4 } \right)  }^{ 3/2 } } } }{ 3 } -4{ { \left( { x+4 } \right)  }^{ 1/2 } } } \right] +c \\ =\dfrac { 2 }{ 3 } { \left( { x+4 } \right) ^{ 3/2 } }-8\sqrt { x+4 } +c \end{array}$$
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Subjective Medium Published on 17th 09, 2020
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