Mathematics

Find : $$\int { \dfrac { { 3x }^{ 2 }-2x+5 }{ x\sqrt { x }  }  } dx$$


SOLUTION
$$\displaystyle\int { \dfrac { { 3 x }^{ 2 }-2 x+5 }{ x\sqrt { x }  }  } d x$$

$$=\int \dfrac{3 x^2-2 x+5}{x^{3/2}}d x=3\int x^{2-3/2}d x-2\int x^{1-3/2}d x+5\int x^{-3/2} d x$$

$$=3\displaystyle\int x^{1/2}d x-2\int x^{-1/2}d x+5\int x^{-3/2} d x$$

$$=3\dfrac{x^{1/2+1}}{1/2+1}-2\dfrac{x^{-1/2+1}}{-1/2+1}+5\dfrac{x^{-3/2+1}}{-3/2+1}+C$$

$$=2 x\sqrt{x}-4\sqrt{x}-10\sqrt{x}+C$$
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Subjective Medium Published on 17th 09, 2020
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