Mathematics

Solve
$$\int {{{dx} \over {\sqrt {5x + 8} }}} $$
using- (a) $$u = 5x+8 $$ (b) $$u = \sqrt {5x + 8} $$


SOLUTION
$$a) u=5{x}+8\implies d{u}=5{d{x}}$$
            $$\displaystyle\int \dfrac{d{x}}{\sqrt{5{x}+8}}=\dfrac{1}{5}\int u^{-1/2}d{u}=\dfrac{2}{5}\sqrt{u}+c=\dfrac{2}{5}\sqrt{5{x}+8}+c$$
$$b) u=\sqrt{5{x}+8}\implies d{u}=\dfrac{5}{2\sqrt{5{x}+8}}d{x}$$
         $$\displaystyle\int \dfrac{d{x}}{\sqrt{5{x}+8}}=\dfrac{2}{5}\displaystyle\int d{u}=\dfrac{2}{5}u+c=\dfrac{2}{5}\sqrt{5{x}+8}+c$$
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Subjective Medium Published on 17th 09, 2020
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