Pertanyaan

∫ cos 3 x d x = ...

$\int cos^{3} x d x = ...$

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Jawaban terverifikasi

Pembahasan

$integral cos cubed space x space d x equals integral cos space x. cos squared x space d x space space space space space space space space space space space space space space space space space space space space space equals integral cos space x left parenthesis 1 minus sin squared x right parenthesis d x space space space space space space space space space space space space space space space space space space space space space equals integral cos space x minus cos space x space sin squared space x space d x M i s a l space u equals sin space x space space space space space space space space space d u equals cos space x space d x space left right double arrow d x equals fraction numerator d u over denominator cos space x end fraction comma space m a k a colon space space space space space space space space space space space space space space equals integral cos space x space d x minus integral cos space x. sin squared space x space d x space space space space space space space space space space space space space space equals sin space x minus integral cos space x. u squared. fraction numerator d u over denominator cos space x end fraction space space space space space space space space space space space space space space equals sin space x minus 1 third u cubed plus C space space space space space space space space space space space space space space equals sin space x minus 1 third sin cubed space x plus C$