Pertanyaan

Hasil dari ∫ x + cos 2 x 1 − sin 2 x d x = ....

Hasil dari $\int \frac{1 - sin 2 x}{x + cos ^{2} x} d x =$ ....

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Misalkan: Maka, Sehingga,

Misalkan:

Maka,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d u over denominator d x end fraction end cell equals cell 1 minus 2 cos invisible function application x sin invisible function application x end cell row cell integral fraction numerator d u over denominator d x end fraction d x end cell equals cell integral 1 minus 2 cos invisible function application x sin invisible function application x d x end cell row cell integral d u end cell equals cell integral 1 minus 2 cos invisible function application x sin invisible function application x d x end cell row cell integral d u end cell equals cell integral 1 minus sin invisible function application 2 x d x end cell end table end style$

Sehingga,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 1 minus sin invisible function application 2 x over denominator x plus cos squared invisible function application x end fraction d x end cell equals cell integral 1 over u d u end cell row blank equals cell ln invisible function application open vertical bar u close vertical bar plus C end cell row blank equals cell ln invisible function application open vertical bar x plus cos squared invisible function application x close vertical bar plus C end cell end table end style$