PLEASE ANSWER CORRECTLY
PLEASE ANSWER CORRECTLY O taff O 2. loge loge o 4. tan- is equal to: 2X+1

Dear student

\int \frac{dx}{(2 x + 1) (1 + \sqrt{2 x + 1})} Put u = 2 x + 1 \Rightarrow dx = \frac{du}{2} = \frac{1}{2} \int \frac{1}{(\sqrt{u} + 1) u} du Now expanding fraction by \frac{1}{u^{\frac{3}{2}}} = \frac{1}{2} \int \frac{1}{(\frac{1}{\sqrt{u}} + 1) u^{\frac{3}{2}}} du Put v = \frac{1}{\sqrt{u}} + 1 \Rightarrow du = - 2 u^{\frac{3}{2}} dv = - \int \frac{1}{v} dv = - logv + C = - \log (\frac{1}{\sqrt{u}} + 1) + C = - \log (\frac{1}{\sqrt{2 x + 1}} + 1) + C = - \log (\frac{1 + \sqrt{2 x + 1}}{\sqrt{2 x + 1}}) + C

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​​PLEASE ANSWER CORRECTLY​​PLEASE ANSWER CORRECTLY O taff O 2. loge loge o 4. tan- is equal to: 2X+1