Pertanyaan

∫ cos 2 8 x 1 − tan 2 8 x cos 4 8 x dx = ....

$\int \frac{1 - tan ^{2} 8 x cos ^{4} 8 x}{cos ^{2} 8 x} dx = ....$

$tan space 8 straight x minus fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction straight x plus sin space 16 straight x plus straight C$
$tan space 8 straight x minus fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction straight x plus fraction numerator begin display style 1 end style over denominator begin display style 16 end style end fraction straight x plus straight C$
$fraction numerator begin display style 1 end style over denominator begin display style 8 end style end fraction tan space 8 straight x minus fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction straight x plus fraction numerator begin display style 1 end style over denominator begin display style 32 end style end fraction sin space 16 straight x plus straight C$
$fraction numerator begin display style 1 end style over denominator begin display style 4 end style end fraction tan space 8 straight x minus fraction numerator begin display style 1 end style over denominator begin display style 6 end style end fraction straight x plus fraction numerator begin display style 1 end style over denominator begin display style 32 end style end fraction sin space 16 straight x plus straight C$

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$fraction numerator 1 over denominator cos space alpha end fraction equals s e c space alpha cos space 2 alpha equals 1 minus 2 space sin to the power of 2 space end exponent alpha integral fraction numerator 1 minus tan squared space 8 x space cos to the power of 4 space 8 x over denominator begin display style cos squared end style begin display style space end style begin display style 8 end style begin display style x end style end fraction d x integral open parentheses fraction numerator 1 over denominator cos squared space 8 x end fraction minus fraction numerator tan squared space 8 x space cos to the power of 4 space 8 x over denominator cos squared space 8 x end fraction close parentheses d x integral open parentheses fraction numerator begin display style 1 end style over denominator begin display style cos squared space 8 x end style end fraction minus tan squared space 8 x. cos squared space 8 x close parentheses d x integral open parentheses s e c squared space 8 x minus fraction numerator begin display style sin squared end style begin display style space end style begin display style 8 end style begin display style x end style over denominator begin display style cos squared end style begin display style space end style begin display style 8 end style begin display style x end style end fraction. cos squared space 8 x close parentheses d x integral open parentheses s e c squared space 8 x minus sin squared space 8 x close parentheses d x integral s e c squared space 8 x space d x minus integral sin squared space 8 x space d x 1 over 8 tan space 8 x minus integral 1 half open parentheses 1 minus cos space 16 x close parentheses d x fraction numerator begin display style 1 end style over denominator begin display style 8 end style end fraction tan space 8 x minus integral fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction d x plus 1 half integral cos space 16 x space d x fraction numerator begin display style 1 end style over denominator begin display style 8 end style end fraction tan space 8 x minus fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction x plus 1 over 32 sin space 16 x plus C$