Mathematics

# Find : $\displaystyle\int {\dfrac{{{\text{si}}{{\text{n}}^{\text{2}}}{\text{x - co}}{{\text{s}}^{\text{2}}}{\text{x}}}}{{{\text{sin}}\;{\text{x}}\;{\text{cos}}\;{\text{x}}}}} \;{\text{dx}}$

##### SOLUTION
$I=\displaystyle\int \dfrac{\sin^2x-\cos^2x}{\sin x\cos x}dx$

$=\displaystyle\int \dfrac{\sin x}{\cos x}dx-\displaystyle\int \dfrac{\cos x}{\sin x}dx$

$=\log|\sec(x)|-\log|\sin x|+c$

$I=\log\dfrac{\sec x}{\sin x}+c$.

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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