∫ x41 dx sama dengan ....

Pertanyaan

$\int\;\frac1{x^4}\;\mathrm dx$ sama dengan ....

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

hasil integral tersebut adalah $negative fraction numerator 1 over denominator 3 straight x cubed end fraction plus straight C$ .

Pembahasan

Ingat kembali:

$integral space ax to the power of straight n space dx equals fraction numerator straight a over denominator straight n plus 1 end fraction straight x to the power of straight n plus 1 end exponent plus straight C$

Maka:

$integral space 1 over x to the power of 4 space straight d x equals integral space x to the power of negative 4 end exponent space straight d x integral space 1 over x to the power of 4 space straight d x equals fraction numerator 1 over denominator negative 4 plus 1 end fraction x to the power of negative 4 plus 1 end exponent plus C integral space 1 over x to the power of 4 space straight d x equals negative 1 third x to the power of negative 3 end exponent plus C integral space 1 over x to the power of 4 space straight d x equals negative fraction numerator 1 over denominator 3 x cubed end fraction plus C$

Jadi, hasil integral tersebut adalah $negative fraction numerator 1 over denominator 3 straight x cubed end fraction plus straight C$ .