Question -20

Calculus Level 3

I want to reduce powers of trigonometric functions when performing integration.

∫ s e c 3 ( 3 x ) d x \displaystyle \int sec^3(3x) \space \mathrm{d}x is equal to :

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1 6 ⋅ [ t a n ( 3 x ) ⋅ s e c 2 ( 3 x ) − l o g ( t a n ( 3 x ) + s e c ( 3 x ) ] + c \frac{1}{6} \cdot [tan(3x) \cdot sec^2(3x)-log(tan(3x)+sec(3x)] +c t a n 2 ( 3 x ) ⋅ s e c ( 3 x ) + l o g ( t a n ( 3 x ) + s e c ( 3 x ) ) + c tan^2(3x) \cdot sec(3x)+log (tan(3x)+sec(3x)) +c 1 6 ⋅ [ t a n ( 3 x ) ⋅ s e c ( 3 x ) + l o g ( t a n ( 3 x ) + s e c ( 3 x ) ) ] + c \frac{1}{6} \cdot [tan(3x) \cdot sec(3x)+log (tan(3x)+sec(3x) ) ] +c 1 6 ⋅ [ t a n ( 3 x ) + l o g ( t a n ( 3 x ) + s e c ( 3 x ) ) ] + c \frac{1}{6} \cdot [tan(3x) +log(tan(3x)+sec(3x))] +c

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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