Pertanyaan

Hasil dari ∫ x 2 − 2 x ( x − 1 ) d x = ....

$Hasil dari \int \frac{( x - 1 )}{x ^{2} - 2 x} d x = ....$

F. Pratama

Master Teacher

Mahasiswa/Alumni Universitas Putra Indonesia YPTK Padang

Jawaban terverifikasi

Pembahasan

$u space equals space x squared space minus space 2 x fraction numerator d u over denominator d x end fraction equals 2 x space minus space 2 space space rightwards double arrow space space d x space equals space fraction numerator d u over denominator 2 x minus 2 end fraction integral fraction numerator x minus 1 over denominator square root of x squared space minus space 2 x end root end fraction d x space equals space integral fraction numerator x minus 1 over denominator square root of u end fraction space fraction numerator d u over denominator 2 x minus 2 end fraction space equals space integral fraction numerator 1 over denominator 2 square root of u end fraction d u space equals space integral 1 half u to the power of negative 1 half end exponent d u space equals space u to the power of 1 half end exponent plus C space equals space square root of x squared minus 2 x end root space plus space C$