Pertanyaan

Nilai dari ∫ 4 x ( 3 x − 5 ) 5 d x adalah ....

Nilai dari $\int 4 x (3 x - 5)^{5} d x$ adalah ....

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Klaim

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

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integral 4 x open parentheses 3 x minus 5 close parentheses to the power of 5 space straight d x equals 1 over 18 x open parentheses 3 x minus 5 close parentheses to the power of 6 minus 4 over 378 open parentheses 3 x minus 5 close parentheses to the power of 7 plus straight C

Pembahasan

Ingat kembali: Diketahui , maka: Sehingga: Jadi, .

Ingat kembali:

integral u space straight d v equals u v minus integral v space straight d u

Diketahui integral space 4 x open parentheses 3 x minus 5 close parentheses to the power of 5 space straight d x , maka:

$u equals 4 x rightwards arrow fraction numerator d u over denominator d x end fraction equals 4 rightwards arrow d u equals 4 space d x straight d v equals open parentheses 3 x minus 5 close parentheses to the power of 5 space straight d x rightwards arrow v equals integral open parentheses 3 x minus 5 close parentheses to the power of 5 space straight d x equals 1 third times 1 over 6 open parentheses 3 x minus 5 close parentheses to the power of 6 plus straight C equals 1 over 18 open parentheses 3 x minus 5 close parentheses to the power of 6 plus straight C$

Sehingga:

Jadi, integral 4 x open parentheses 3 x minus 5 close parentheses to the power of 5 space straight d x equals 1 over 18 x open parentheses 3 x minus 5 close parentheses to the power of 6 minus 4 over 378 open parentheses 3 x minus 5 close parentheses to the power of 7 plus straight C .