Question

$\huge\mathcal{\fcolorbox{aqua}{azure}{\pink{♡QuEstion}}}$
Interegate:-
$\ \textless \ br /\ \textgreater \ \ \textless \ br /\ \textgreater \ \displaystyle \sf \: \int \dfrac{ \sin^{2}x - \cos ^{2} x}{ \sin \: x. \cos \: x}$

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Answer 1

Question:-

$\sf \large \int \dfrac{ sin^{2}x - cos ^{2} x}{ sin \: x. cos \: x}$

Solution:-

$\sf \large \int \frac{sin { }^{2}x - cos {}^{2} x}{sin \: x.cos \: x} dt = \sf \large \int \bigg( \frac{sin \: x}{cos \: x} - \frac{cos \: x}{sin \: x} \bigg)dx$

$\sf \large = \int tan \: xdx - \int cot \: xdx$

$\sf \large = log |sec \: x| - log |sin \: x| + c.$

Answer:-

${ \boxed{ \sf \large \red{\sf \large \int \dfrac{ sin^{2}x - cos ^{2} x}{ sin \: x. cos \: x} \sf \large = log |sec \: x| - log |sin \: x| + c.}}}$

Hope you have satisfied. ⚘