Selesaikan setiap integral berikut. ∫5x2dx

Pertanyaan

Selesaikan setiap integral berikut.

$\style{font-size:14px}{\int\sqrt[5]{x^2}dx}$

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

. hasil dari begin mathsize 14px style integral fifth root of x squared end root d x end style

adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 7 x fifth root of x squared end root plus c end cell end table

Pembahasan

Ingat kembali rumus integral tak tentu berikut.

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

Sehingga, diperoleh perhitungan berikut ini.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fifth root of x squared end root d x end cell equals cell integral x to the power of 2 over 5 end exponent d x end cell row blank equals cell fraction numerator 1 over denominator begin display style 2 over 5 end style plus 1 end fraction x to the power of 2 over 5 plus 1 end exponent plus c end cell row blank equals cell 5 over 7 x to the power of 7 over 5 end exponent plus c end cell row blank equals cell 5 over 7 x fifth root of x squared end root plus c end cell end table end style$

Jadi. hasil dari begin mathsize 14px style integral fifth root of x squared end root d x end style adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 7 x fifth root of x squared end root plus c end cell end table .