Pertanyaan

Tentukan integral dari ∫ x 2 2 + 3 x d x = ...

Tentukan integral dari $\int \frac{2}{x ^{2}} + 3 x d x = ...$

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

.

$integral 2 over x squared plus 3 square root of x space d x equals negative fraction numerator 2 over denominator 3 x end fraction plus 2 x square root of x plus C$ .

Pembahasan

Cara pengerjaan integral tak tentu adalah . Maka: Jadi .

Cara pengerjaan integral tak tentu adalah $integral straight a x to the power of straight n space d x equals fraction numerator a over denominator straight n plus 1 end fraction x to the power of straight n plus 1 end exponent plus C$ .

Maka:

$integral 2 over x squared plus 3 square root of x space d x equals integral 2 x to the power of negative 2 end exponent plus 3 x to the power of 1 half end exponent space d x equals fraction numerator 2 over denominator negative 2 plus 1 end fraction x to the power of negative 1 end exponent plus fraction numerator 3 over denominator begin display style 1 half end style plus 1 end fraction x to the power of 3 over 2 end exponent plus C equals negative 2 over 3 x to the power of negative 1 end exponent plus 2 x to the power of 3 over 2 end exponent plus C equals negative fraction numerator 2 over denominator 3 x end fraction plus 2 x square root of x plus C$

Jadi $integral 2 over x squared plus 3 square root of x space d x equals negative fraction numerator 2 over denominator 3 x end fraction plus 2 x square root of x plus C$ .