Pertanyaan

Tentukan hasil dari ∫ 4 ( x 3 − 15 x 2 − 18 ) 3 6 x ( x − 10 ) d x .

Tentukan hasil dari $\int \frac{6 x ( x - 10 )}{4 ( x ^{3} - 15 x ^{2} - 18 ) ^{3}} d x$ .

J. Joko

Master Teacher

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 6 x open parentheses x minus 10 close parentheses over denominator fourth root of open parentheses x cubed minus 15 x squared minus 18 close parentheses cubed end root end fraction d x end cell equals cell integral fraction numerator 6 x open parentheses x minus 10 close parentheses over denominator 3 x open parentheses x minus 10 close parentheses open parentheses x cubed minus 15 x squared minus 18 close parentheses to the power of bevelled 3 over 4 end exponent end fraction d open parentheses x cubed minus 15 x squared minus 18 close parentheses end cell row blank equals cell 2 integral open parentheses x cubed minus 15 x squared minus 18 close parentheses to the power of negative bevelled 3 over 4 end exponent d open parentheses x cubed minus 15 x squared minus 18 close parentheses end cell row blank equals cell 2 times 4 fourth root of x cubed minus 15 x squared minus 18 end root plus C end cell row blank equals cell 8 fourth root of x cubed minus 15 x squared minus 18 end root plus C comma space text dengan end text space C space text konstanta end text end cell end table end style$