Mathematics

# Solve:$\displaystyle \int {\dfrac{{2 - 3\sin x}}{{{{\cos }^2}x}}} dx.$

##### SOLUTION

$\int \dfrac{\left( 2-3sinx \right)}{co{{s}^{2}}x}dx$

$=\int{\left( \dfrac{2}{{{\cos }^{2}}x}-\dfrac{3\sin x}{{{\cos }^{2}}x} \right)dx}$

$=\int{2{{\sec }^{2}}xdx-\int{3\dfrac{\sin x}{\cos x}\dfrac{1}{\cos x}}dx}$

$=2\int{{{\sec }^{2}}xdx-3\int{\sec x\tan xdx}}$

$=2\operatorname{tanx}-3secx+C$

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

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