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Nilai dari ∫ ( ( 54 x + 63 ) sin 3 ( 3 x 2 + 7 x − 1 ) . cos ( 3 x 2 + 7 x − 1 ) ) d x adalah...

Nilai dari $\int ((54 x + 63) sin^{3} (3 x^{2} + 7 x - 1) . cos (3 x^{2} + 7 x - 1)) d x$ adalah...

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Misalkan , maka Sehingga bentuk integral menjadi

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, maka

$fraction numerator d u over denominator d x end fraction space equals space open parentheses 6 x space plus space 7 close parentheses space cos space open parentheses 3 x squared space plus 7 x space minus space 1 close parentheses d x space equals space fraction numerator d u over denominator open parentheses 6 x space plus space 7 close parentheses begin display style space end style begin display style cos end style begin display style space end style begin display style open parentheses 3 x squared space plus 7 x space minus space 1 close parentheses end style end fraction$

Sehingga bentuk integral menjadi

$integral open parentheses 9 open parentheses 6 x space plus space 7 close parentheses space u cubed space. space cos space open parentheses 3 x squared space plus space 7 x space minus space 1 close parentheses close parentheses fraction numerator d u over denominator open parentheses 6 x space plus space 7 close parentheses cos open parentheses 3 x squared space plus space 7 x space minus space 1 close parentheses end fraction integral 9 u cubed d u space equals space 9 over 4 u to the power of 4 space plus space C equals space 9 over 4 space sin to the power of 4 space open parentheses 3 x squared space plus space 7 x space minus space 1 close parentheses space plus space C$