RoboguruRoboguru
SD

∫ (x2+1)3 x2 dx=...

Pertanyaan

begin mathsize 14px style integral space open parentheses x squared plus 1 close parentheses cubed space x squared space straight d x equals... end style

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

diperoleh hasilnya adalah begin mathsize 14px style 1 over 9 x to the power of 9 plus 3 over 7 x to the power of 7 plus 3 over 5 x to the power of 5 plus 1 third x cubed plus c end style.

Pembahasan

Gunakan konsep integral tak tentu.

begin mathsize 14px style integral a x to the power of n space straight 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 end style 

Untuk menyelesaikan soal di atas terlebih dahulu selesaikan perpangkatan dan perkaliannya.

Perhatikan perhitungan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell integral open parentheses x squared plus 1 close parentheses cubed x squared space straight d x end cell equals cell integral open parentheses x squared plus 1 close parentheses open parentheses x squared plus 1 close parentheses open parentheses x squared plus 1 close parentheses x squared space straight d x end cell row blank equals cell integral open parentheses x to the power of 4 plus 2 x squared plus 1 close parentheses open parentheses x squared plus 1 close parentheses x squared space straight d x end cell row blank equals cell integral open parentheses x to the power of 6 plus 3 x to the power of 4 plus 3 x squared plus 1 close parentheses x squared space straight d x end cell row blank equals cell integral open parentheses x to the power of 8 plus 3 x to the power of 6 plus 3 x to the power of 4 plus x squared close parentheses space straight d x end cell row cell integral open parentheses x squared plus 1 close parentheses cubed x squared space straight d x end cell equals cell 1 over 9 x to the power of 9 plus 3 over 7 x to the power of 7 plus 3 over 5 x to the power of 5 plus 1 third x cubed plus c end cell end table end style 

Jadi, diperoleh hasilnya adalah begin mathsize 14px style 1 over 9 x to the power of 9 plus 3 over 7 x to the power of 7 plus 3 over 5 x to the power of 5 plus 1 third x cubed plus c end style.

94

1.0 (1 rating)

Denny Malik

Jawaban tidak sesuai

Pertanyaan serupa

Nilai integral dari ∫x+5 dx adalah ...

341

5.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia