Iklan

Iklan

Pertanyaan

∫ x + 3 ​ x ​ d x = ...

 

Iklan

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

.

  integral fraction numerator x over denominator square root of x plus 3 end root end fraction d x equals space 2 over 3 open parentheses x plus 3 close parentheses square root of x plus 3 end root minus 6 square root of x plus 3 end root plus C

Iklan

Pembahasan

Misalkan , maka Sehingga Dengan demikian, .

Misalkan u equals x plus 3, maka 

u equals x plus 3 space rightwards double arrow space x equals u minus 3 space space space space space space space space space space space space space space space space rightwards double arrow space straight d open parentheses x close parentheses equals straight d open parentheses u minus 3 close parentheses space space space space space space space space space space space space space space space space rightwards double arrow space straight d x equals straight d u space   

Sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator x over denominator square root of x plus 3 end root end fraction d x end cell equals cell integral fraction numerator u minus 3 over denominator square root of u end fraction d u end cell row blank equals cell integral open parentheses fraction numerator u over denominator square root of u end fraction minus fraction numerator 3 over denominator square root of u end fraction close parentheses d u end cell row blank equals cell integral open parentheses u over u to the power of begin display style 1 half end style end exponent minus 3 over u to the power of 1 half end exponent close parentheses d u end cell row blank equals cell integral open parentheses u to the power of 1 half end exponent minus 3 u to the power of negative 1 half end exponent close parentheses d u end cell row blank equals cell fraction numerator 1 over denominator begin display style 3 over 2 end style end fraction u to the power of 3 over 2 end exponent minus 3 times fraction numerator 1 over denominator begin display style 1 half end style end fraction u to the power of 1 half end exponent plus C end cell row blank equals cell 2 over 3 u to the power of 3 over 2 end exponent minus 6 u to the power of 1 half end exponent plus C end cell row blank equals cell 2 over 3 u square root of u minus 6 square root of u plus C end cell row blank equals cell 2 over 3 open parentheses x plus 3 close parentheses square root of x plus 3 end root minus 6 square root of x plus 3 end root plus C end cell end table 

Dengan demikian,  integral fraction numerator x over denominator square root of x plus 3 end root end fraction d x equals space 2 over 3 open parentheses x plus 3 close parentheses square root of x plus 3 end root minus 6 square root of x plus 3 end root plus C

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

3

Iklan

Iklan

Pertanyaan serupa

Hasil dari adalah ....

1

0.0

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

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia