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Pertanyaan

Carilah  nilai integral berikut!

integral fraction numerator 4 x to the power of 5 plus x cubed minus 2 over denominator x end fraction d x

A. Fatta

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

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.

Pembahasan

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.

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