Pertanyaan

Selesaikanlah. ∫ ( 9 x + 11 ) 5 d x

Selesaikanlah.

$\int (9 x + 11)^{5} d x$

L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Ingat, Untuk menyelesaikan soal di atas, kita gunakan integral substitusi. Misal: Sehingga, Jadi, .

Ingat,

$integral a x to the power of n d x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus c$

Untuk menyelesaikan soal di atas, kita gunakan integral substitusi.

Misal:

$u equals 9 x plus 11 space space space space space space rightwards arrow space space space space space fraction numerator d u over denominator d x end fraction equals 9 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space d x equals fraction numerator d u over denominator 9 end fraction$

Sehingga,

$integral open parentheses 9 x plus 11 close parentheses to the power of 5 space d x equals integral u to the power of 5 space fraction numerator d u over denominator 9 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 over 9 integral u to the power of 5 space d u space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 over 9.1 over 6 u to the power of 6 plus c space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 over 54 open parentheses 9 x plus 11 close parentheses to the power of 6 plus c$

Jadi, .