Iklan

Iklan

Pertanyaan

Hasil dari ∫ x ​ ( 2 x − 1 ) ( x + 2 ) ​ d x adalah ...

Hasil dari  adalah ...space 

Iklan

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

.

 integral fraction numerator open parentheses 2 x minus 1 close parentheses open parentheses x plus 2 close parentheses over denominator square root of x end fraction space straight d x equals 4 over 5 x squared square root of x plus 2 x square root of x minus 4 square root of x plus C.

Iklan

Pembahasan

Ingat! Maka, hasildari adalah: Jadi, .

Ingat!

table attributes columnalign right center left columnspacing 0px end attributes row cell integral a x to the power of n space straight d x end cell equals cell fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus C end cell row cell integral open parentheses f open parentheses x close parentheses plus-or-minus g open parentheses x close parentheses close parentheses space straight d x end cell equals cell integral f open parentheses x close parentheses space straight d x plus-or-minus integral g open parentheses x close parentheses space straight d x end cell row cell integral k times f open parentheses x close parentheses space straight d x end cell equals cell k integral f open parentheses x close parentheses space straight d x end cell end table   

Maka, hasil dari integral fraction numerator open parentheses 2 x minus 1 close parentheses open parentheses x plus 2 close parentheses over denominator square root of x end fraction space straight d x adalah:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral fraction numerator open parentheses 2 x minus 1 close parentheses open parentheses x plus 2 close parentheses over denominator square root of x end fraction space straight d x end cell row blank equals cell integral x to the power of negative 1 half end exponent open parentheses 2 x minus 1 close parentheses open parentheses x plus 2 close parentheses space straight d x end cell row blank equals cell integral open parentheses 2 x to the power of 1 half end exponent minus x to the power of negative 1 half end exponent close parentheses open parentheses x plus 2 close parentheses space straight d x end cell row blank equals cell integral 2 x to the power of 3 over 2 end exponent plus 3 x to the power of 1 half end exponent minus 2 x to the power of negative 1 half end exponent space d x end cell row blank equals cell 2 integral x to the power of 3 over 2 end exponent space d x plus 3 integral x to the power of 1 half end exponent space d x minus 2 integral x to the power of negative 1 half end exponent space d x end cell row blank equals cell fraction numerator 2 over denominator begin display style bevelled 5 over 2 end style end fraction x to the power of 5 over 2 end exponent plus fraction numerator 3 over denominator begin display style bevelled 3 over 2 end style end fraction x to the power of 3 over 2 end exponent minus fraction numerator 2 over denominator begin display style bevelled 1 half end style end fraction x to the power of 1 half end exponent plus C end cell row blank equals cell 4 over 5 x squared square root of x plus 2 x square root of x minus 4 square root of x plus C end cell end table  

Jadi, integral fraction numerator open parentheses 2 x minus 1 close parentheses open parentheses x plus 2 close parentheses over denominator square root of x end fraction space straight d x equals 4 over 5 x squared square root of x plus 2 x square root of x minus 4 square root of x plus C.

25

Iklan

Iklan

Pertanyaan serupa

Tentukan integral dari ∫ ( 2 x 2 − 3 x + 1 ) d x .

52

5.0

Jawaban terverifikasi

Iklan

Iklan

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

Fitur Roboguru

Topik Roboguru

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