Integral Calculus> integrate the following integral ∫ 1 / 1 ...

integrate the following integral
∫ 1 / 1 – sin x/2 dx

taniska , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int \frac{1}{1-sin\frac{x}{2}}dx$
$I = \int \frac{(1+sin\frac{x}{2})}{(1-sin\frac{x}{2})(1+sin\frac{x}{2})}dx$
$I = \int \frac{(1+sin\frac{x}{2})}{(1-sin^{2}\frac{x}{2})}dx$
$I = \int \frac{(1+sin\frac{x}{2})}{cos^{2}\frac{x}{2} }dx$
$I = \int (sec^{2}\frac{x}{2}+sec\frac{x}{2}tan\frac{x}{2})dx$
$I = \int sec^{2}\frac{x}{2}dx+\int sec\frac{x}{2}tan\frac{x}{2}dx$
$I = 2tan\frac{x}{2}+\int sec\frac{x}{2}tan\frac{x}{2}dx$
$I = 2tan\frac{x}{2}+2sec\frac{x}{2}+c$