Find the following integrals- 2 x-cosec2 x d x-

∫sec^2x/cosec^2 xdx =∫sin^2x/cos^2 xdx =∫ tan^2 x dx =∫ (sec^2 x 1)dx ( ∵1/cosec^2 x=sin^2 x and sec^2x=1/cos^2 x ) =∫ sec^2 x dx ∫ 1 dx =tan x x + C ...

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Byju's Answer

Standard XII

Mathematics

Standard Formulae - 2

Find the foll...

Question

Find the following integrals.
$\int \frac{s e c^{2} x}{c o s e c^{2} x} d x .$

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Solution

$\int \frac{s e c^{2} x}{c o s e c^{2} x} d x = \int \frac{s i n^{2} x}{c o s^{2} x} d x = \int t a n^{2} x d x = \int (s e c^{2} x - 1) d x (∵ \frac{1}{c o s e c^{2} x} = s i n^{2} x a n d s e c^{2} x = \frac{1}{c o s^{2} x}) = \int s e c^{2} x d x - \int 1 d x = t a n x - x + C$

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Find the following integrals. ∫sec2xcosec2xdx.

∫sec2xcosec2xdx=∫sin2xcos2xdx=∫tan2xdx=∫(sec2x−1)dx(∵1cosec2x=sin2x and sec2x=1cos2x)=∫sec2xdx−∫1dx=tanx−x+C

Find the following integrals.
$\int \frac{s e c^{2} x}{c o s e c^{2} x} d x .$

$\int \frac{s e c^{2} x}{c o s e c^{2} x} d x = \int \frac{s i n^{2} x}{c o s^{2} x} d x = \int t a n^{2} x d x = \int (s e c^{2} x - 1) d x (∵ \frac{1}{c o s e c^{2} x} = s i n^{2} x a n d s e c^{2} x = \frac{1}{c o s^{2} x}) = \int s e c^{2} x d x - \int 1 d x = t a n x - x + C$