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Question Number 84326 by sahnaz last updated on 11/Mar/20

$$\int \frac{3-7\mathrm{u}}{{7\mathrm{u}}^2-7}\mathrm{du}$$

Answered by TANMAY PANACEA last updated on 11/Mar/20

$$\frac{3}{7}\int \frac{du}{(u+1)(u-1)}-\frac{1}{2}\int \frac{d(7u^2-7)}{7u^2-7}$$$$\frac{3}{7\times 2}\int \frac{(u+1)-(u-1)}{(u+1)(u-1)}du-\frac{1}{2}\int \frac{d(7u^2-7)}{7u^2-7}$$$$\frac{3}{14}[\int \frac{du}{u-1}-\int \frac{du}{u+1}]-\frac{1}{2}\int \frac{d(7u^2-7)}{7u^2-7}$$$$\frac{3}{14}\left[ln\left(\frac{u-1}{u+1}\right)\right]-\frac{1}{2}ln(7u^2-7)+c$$$$\frac{3}{14}ln\left(\frac{u-1}{u+1}\right)-\frac{1}{2}\{ln7+ln(u^2-1)\}+c$$$$\frac{3}{14}ln\left(\frac{u-1}{u+1}\right)-\frac{1}{2}ln(u^2-1)+C_1$$

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