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Pertanyaan

Tentukan integral-integral tak tentu berikut ini.

b) begin mathsize 14px style integral fraction numerator 1 over denominator cube root of x to the power of 5 end root end fraction straight d x end style  

E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

nilai dari begin mathsize 14px style integral fraction numerator 1 over denominator cube root of x to the power of 5 end root end fraction straight d x end style adalah begin mathsize 14px style fraction numerator 3 over denominator 2 cube root of x squared end root end fraction plus C end style.

Pembahasan

Integral tak tentu merupakan sebuah bentuk operas pengintegralan pada suatu fungsi menghasilkan suatu fungsi baru.

Nilai dari begin mathsize 14px style integral fraction numerator 1 over denominator cube root of x to the power of 5 end root end fraction straight d x end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 1 over denominator cube root of x to the power of 5 end root end fraction straight d x end cell equals cell integral 1 over x to the power of 5 over 3 end exponent straight d x end cell row blank equals cell integral x to the power of negative begin inline style 5 over 3 end style end exponent straight d x end cell row blank equals cell negative 3 over 2 x to the power of negative begin inline style 5 over 3 plus 1 end style end exponent plus C end cell row blank equals cell negative 3 over 2 x to the power of negative begin inline style 2 over 3 end style end exponent plus C end cell row blank equals cell negative fraction numerator 3 over denominator 2 cube root of x squared end root end fraction plus C end cell end table end style      

Jadi, nilai dari begin mathsize 14px style integral fraction numerator 1 over denominator cube root of x to the power of 5 end root end fraction straight d x end style adalah begin mathsize 14px style fraction numerator 3 over denominator 2 cube root of x squared end root end fraction plus C end style.

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