Question

integrate (secx/b+a tanx)dx

Answer 1

$\textbf{Formula used:}$

$\begin{array}{|c|}\cline{1-1}\\\int{secx}\;dx=log|secx+tanx|+c\\\cline{1-1}\\\int{tanx}\;dx=log|secx|+c\\\cline{1-1}\end{array}$

$\text{Now,}$

$\int\,(\frac{secx}{b}+a\,tanx)dx$

$=\frac{1}{b}\int\,secx\,dx+a\int\,tanx\,dx$

$=\frac{1}{b}\,log|secx+tanx|+a\,log|secx|+c$

$\therefore\bf\int\,(\frac{secx}{b}+a\,tanx)dx=\frac{1}{b}\,log|secx+tanx|+a\,log|secx|+c$

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