The correct option is B #10; xtanx+c #10; ∫2x+sin2x1+cos2xdx ∫2x+sin2x2cos^2xdx ∫ xsec^2x^dx+∫ tanxdx x∫ sec^2xdx ∫ (∫ sec^2xdx)d ...

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Integration by Parts

∫2x+sin2x/1+c...

Question

$\int \frac{2 x + s i n 2 x}{1 + c o s 2 x} d x =$

x s i n 2 x + c

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- x t a n x + c

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x s e c x + c

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x t a n x + c

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Solution

The correct option is B $x t a n x + c$
$\int \frac{2 x + s i n 2 x}{1 + c o s 2 x} d x$
$\int \frac{2 x + s i n 2 x}{2 c o s^{2} x} d x$
$\int x s e c^{2} x^{d x} + \int t a n x d x$
$x \int s e c^{2} x d x - \int (\int s e c^{2} x d x) d x$ $+ \int t a n x d x$
$x \int s e c^{2} x d x - \int t a n x d x + \int t a n x d x$
$x t a n x + c$
$\int \frac{2 x + s i n 2 x}{1 + c o s 2 x} = x t a n x + c$

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