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Question Number 49225 by AdqhK ÐQeQqQ last updated on 04/Dec/18

$$\int \frac{1}{z(z^{17}+1)}=??findplease$$

Answered by arvinddayama01@gmail.com. last updated on 04/Dec/18

$$\int \frac{1}{z(z^{17}+1)}.\frac{z^{16}}{z^{16}}dz$$$$z^{17}=t$$$$d.w.r.toz$$$$z^{16}dz=\frac{1}{17}dt$$$$\frac{1}{17}\int \frac{dt}{t(t+1)}$$$$\frac{1}{17}\int [\frac{1}{t}-\frac{1}{t+1}]dt$$$$\frac{1}{17}ln\left(\frac{t}{t+1}\right)+C$$$$\frac{1}{17}ln\left(\frac{z^{17}}{z^{17}+1}\right)+C$$$$\because \int \frac{1}{x(x^n+1)}dx=\frac{1}{n}ln\left(\frac{x^n}{x^n+1}\right)+C$$

Commented by AdqhK ÐQeQqQ last updated on 04/Dec/18

$$thankusir$$$$$$

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