Find the integrals of the functions-sin 3 x-cos 3 x-sin 2 x cos 2 x d x

∫sin^3 x+cos^3x/sin^2 x cos^2 xdx.=∫sin^3 x/sin^2 x cos^2 xdx +∫cos^3 x/sin^2 x cos^2 xdx =∫sin x/cos x cos xdx +∫cos x/sin x sin xdx =∫ tan x.sec x dx+∫ cot ...

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Standard XII

Mathematics

Range of Trigonometric Expressions

Find the inte...

Question

Find the integrals of the functions.
$\int \frac{s i n^{3} x + c o s^{3} x}{s i n^{2} x c o s^{2} x} d x .$

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Solution

$\int \frac{s i n^{3} x + c o s^{3} x}{s i n^{2} x c o s^{2} x} d x . = \int \frac{s i n^{3} x}{s i n^{2} x c o s^{2} x} d x + \int \frac{c o s^{3} x}{s i n^{2} x c o s^{2} x} d x = \int \frac{s i n x}{c o s x c o s x} d x + \int \frac{c o s x}{s i n x s i n x} d x = \int t a n x . s e c x d x + \int c o t x . c o s e c x d x = s e c x - c o s e c x + C$

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Find the integrals of the functions. ∫sin3x+cos3xsin2x cos2xdx.

∫sin3x+cos3xsin2x cos2xdx.=∫sin3xsin2x cos2xdx+∫cos3xsin2xcos2xdx=∫sinxcosx cosxdx+∫cosxsinx sinxdx=∫tanx.secxdx+∫cotx.cosecxdx=secx−cosecx+C

Find the integrals of the functions.
$\int \frac{s i n^{3} x + c o s^{3} x}{s i n^{2} x c o s^{2} x} d x .$