Pertanyaan

∫ 3 ( 3 x + 5 ) 5 d x = ....

$\int 3 (3 x + 5)^{5} d x = ....$

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Klaim

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Ingat rumus: Sehingga diperoleh

Ingat rumus:

$integral left parenthesis a x plus b right parenthesis to the power of n equals 1 over a. space fraction numerator 1 over denominator left parenthesis n plus 1 right parenthesis end fraction left parenthesis a x plus b right parenthesis to the power of n plus 1 end exponent plus C$

Sehingga diperoleh

$integral cube root of left parenthesis 3 x plus 5 right parenthesis to the power of 5 end root space d x equals integral left parenthesis 3 x plus 5 right parenthesis to the power of 5 over 3 end exponent d x equals fraction numerator 1 over denominator begin display style 5 over 3 end style plus 1 end fraction. space 1 third left parenthesis 3 x plus 5 right parenthesis to the power of 5 over 3 plus 1 end exponent plus C equals fraction numerator up diagonal strike 3 over denominator 8 end fraction. fraction numerator 1 over denominator up diagonal strike 3 end fraction plus left parenthesis 3 x plus 5 right parenthesis to the power of 5 over 3 plus 1 end exponent plus C equals 1 over 8 space left parenthesis 3 x plus 5 right parenthesis to the power of 2 plus 2 over 3 end exponent plus C equals 1 over 8 space left parenthesis 3 x plus 5 right parenthesis squared space left parenthesis 3 x plus 5 right parenthesis to the power of 2 over 3 end exponent plus C equals 1 over 8 space left parenthesis 3 x plus 5 right parenthesis squared space space cube root of left parenthesis 3 x plus 5 right parenthesis squared end root plus C$