∫ 53x2​(3x2+2)2x​​ dx

Pertanyaan

integral space fraction numerator open parentheses 3 x squared plus 2 close parentheses squared square root of x over denominator 5 cube root of x squared end root end fraction space straight d x

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

hasil dari integral space fraction numerator open parentheses 3 x squared plus 2 close parentheses squared square root of x over denominator 5 cube root of x squared end root end fraction space straight d x adalah 3 over 5 cube root of x squared end root open parentheses 9 over 14 x to the power of 4 plus 3 over 2 x squared plus 2 close parentheses plus c.

Pembahasan

Ingat sifat-sifat operasi bentuk pangkat sebagai berikut

  • a to the power of n cross times a to the power of m equals a to the power of n plus m end exponent
  • a to the power of n over a to the power of m equals a to the power of n minus m end exponent
  • open parentheses a to the power of n close parentheses to the power of m equals a to the power of n cross times m end exponent
  • m-th root of a to the power of n end root equals a to the power of n over m end exponent

Rumus dasar integral adalah sebagai berikut

integral a x to the power of n space straight d x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent space plus c

Perhatikan perhitungan berikut

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral space fraction numerator open parentheses 3 x squared plus 2 close parentheses squared square root of x over denominator 5 cube root of x squared end root end fraction space straight d x end cell row blank equals cell integral fraction numerator open parentheses 3 x squared plus 2 close parentheses open parentheses 3 x squared plus 2 close parentheses x to the power of begin display style 1 half end style end exponent over denominator 5 x to the power of begin display style 2 over 3 end style end exponent end fraction space straight d x end cell row blank equals cell 1 fifth integral open parentheses 9 x to the power of 4 plus 12 x squared plus 4 close parentheses x to the power of 1 half end exponent x to the power of negative 2 over 3 end exponent space straight d x end cell row blank equals cell 1 fifth integral open parentheses 9 x to the power of 4 plus 12 x squared plus 4 close parentheses x to the power of 1 half minus 2 over 3 end exponent space straight d x end cell row blank equals cell 1 fifth integral open parentheses 9 x to the power of 4 plus 12 x squared plus 4 close parentheses x to the power of negative 1 third end exponent space straight d x end cell row blank equals cell 1 fifth integral open parentheses 9 x to the power of 4 times x to the power of negative 1 third end exponent plus 12 x squared times x to the power of negative 1 third end exponent plus 4 x to the power of negative 1 third end exponent close parentheses space straight d x end cell row blank equals cell 1 fifth integral open parentheses 9 x to the power of 11 over 3 end exponent plus 12 x to the power of 5 over 3 end exponent plus 4 x to the power of negative 1 third end exponent close parentheses space straight d x end cell row blank equals cell 1 fifth open parentheses fraction numerator 9 over denominator begin display style 14 over 3 end style end fraction x to the power of 14 over 3 end exponent plus fraction numerator 12 over denominator begin display style 8 over 3 end style end fraction x to the power of 8 over 3 end exponent plus fraction numerator 4 over denominator begin display style 2 over 3 end style end fraction x to the power of 2 over 3 end exponent close parentheses plus c end cell row blank equals cell 1 fifth open parentheses 27 over 14 x to the power of 4 2 over 3 end exponent plus 36 over 8 x to the power of 2 2 over 3 end exponent plus 12 over 2 x to the power of 2 over 3 end exponent close parentheses plus c end cell row blank equals cell 1 fifth open parentheses 27 over 14 x to the power of 4 x to the power of 2 over 3 end exponent plus 9 over 2 x squared x to the power of 2 over 3 end exponent plus 6 x to the power of 2 over 3 end exponent close parentheses plus c end cell row blank equals cell 3 over 5 x to the power of 2 over 3 end exponent open parentheses 9 over 14 x to the power of 4 plus 3 over 2 x squared plus 2 close parentheses plus c end cell row blank equals cell 3 over 5 cube root of x squared end root open parentheses 9 over 14 x to the power of 4 plus 3 over 2 x squared plus 2 close parentheses plus c end cell end table

Dengan demikian hasil dari integral space fraction numerator open parentheses 3 x squared plus 2 close parentheses squared square root of x over denominator 5 cube root of x squared end root end fraction space straight d x adalah 3 over 5 cube root of x squared end root open parentheses 9 over 14 x to the power of 4 plus 3 over 2 x squared plus 2 close parentheses plus c.

29

4.6 (3 rating)

Marila Diva Juliyanda

Makasih ❤️

Pertanyaan serupa

Carilah integral tak tentu berikut ini. b.∫(x2x4−2x3+1​)dx

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