Pertanyaan

Carilah nilai integral berikut! ∫ x 4 x 5 + x 3 − 2 d x

Carilah nilai integral berikut!

$\int \frac{4 x ^{5} + x ^{3} - 2}{x} d x$

A. Fatta

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

nilai integral dari adalah .

nilai integral dari $integral fraction numerator 4 x to the power of 5 plus x cubed minus 2 over denominator x end fraction d x$ adalah 4 over 5 x to the power of 5 plus 1 third x cubed minus 2 ln open vertical bar x close vertical bar plus c

4 over 5 x to the power of 5 plus 1 third x cubed minus 2 ln open vertical bar x close vertical bar plus c

Pembahasan

Perhatikan perhitungan berikut! Ingat bahwa Sehingga Dengan demikian, nilai integral dari adalah .

Perhatikan perhitungan berikut!

Ingat bahwa

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral a x to the power of n d x end cell equals cell fraction numerator 1 over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus c end cell row cell integral 1 over x d x end cell equals cell ln open vertical bar x close vertical bar plus c end cell end table$

Sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 4 x to the power of 5 plus x cubed minus 2 over denominator x end fraction d x end cell equals cell integral open parentheses 4 x to the power of 4 plus x squared minus 2 over x close parentheses d x end cell row blank equals cell 4 over 5 x to the power of 5 plus 1 third x cubed minus 2 ln open vertical bar x close vertical bar plus c end cell end table$

Dengan demikian, nilai integral dari $integral fraction numerator 4 x to the power of 5 plus x cubed minus 2 over denominator x end fraction d x$ adalah 4 over 5 x to the power of 5 plus 1 third x cubed minus 2 ln open vertical bar x close vertical bar plus c .