Ingat sifat-sifat operasi bentuk pangkat sebagai berikut Rumus dasar integral adalah sebagai berikut Perhatikan perhitungan berikut Dengan demikian hasil dari adalah .

∫ 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

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

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 .