We are given, I=∫( 1+2sinx / cos^ 2 x #160; ) #160; dx #160;I=∫( sec^ 2 x+2tanx.secx ) #160; dx #160; #160; as we know , 1 ...

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Basic Trigonometric Identities

∫1+2sin xcos2...

Question

$\int (\frac{1 + 2 sin x}{{cos}^{2} x}) d x$ .

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Solution

we are given, $I = \int (\frac{1 + 2 s i n x}{c o s^{2} x}) d x$

$I = \int (s e c^{2} x + 2 t a n x . s e c x) d x$

$a s w e k n o w, \frac{1}{c o s θ} = s e c θ$ & $\frac{s i n θ}{c o s θ} = t a n θ$

$I = \int s e c^{2} x d x + 2 \int t a n x . s e c x d x$

$I = t a n x + 2 s e c x + c$

$s o, \int (\frac{1 + 2 sin x}{c o s^{2} x}) d x = t a n x + 2 s e c x + c$

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Similar questions

\int_{0}^{π / 2} \frac{sin x}{1 + {cos}^{2} x} d x

π / 2 \int 0 \frac{sin x}{1 + {cos}^{2} x} d x

\int_{- π / 2}^{π / 2} sin x \sqrt{1 - {cos}^{2} x} d x

{\int_{0}}^{π / 2} \frac{sin x}{1 + c o s^{2} x} d x

Evaluate the integrals using substitution.
$\int_{0}^{\frac{π}{2}} \frac{s i n x}{1 + c o s^{2} x} d x .$

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