A] ∫1/cos(sin^ 1x)dx Let sin^ 1x = t ⇒ #160; sint = x Cost dt = dx #160;substituting dx = cost dt ⇒∫1/cos t× cos t dt. ⇒∫ dt ⇒ #16 ...

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Functions

Solve ∫dxcos...

Question

Solve
$\int \frac{d x}{cos ({sin}^{- 1} x)}$ .

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Solution

A] $\int \frac{1}{c o s (s i n^{- 1} x)} d x$
Let $s i n^{- 1} x = t \Rightarrow s i n t = x$
Cost dt = dx
substituting dx = cost dt
$\Rightarrow \int \frac{1}{c o s t} \times c o s t d t .$
$\Rightarrow \int d t$
$\Rightarrow t + c$
$\Rightarrow s i n^{- 1} x + c$

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