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Hasil integral fraction numerator 2 over denominator 3 cube root of 2 x end root end fraction d x equals ...

Pembahasan Soal:

Operasi integral tak tentu, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 2 over denominator 3 cube root of 2 x end root end fraction d x end cell equals cell 2 over 3 integral fraction numerator 1 over denominator cube root of 2 x end root end fraction d x end cell row blank equals cell 2 over 3 integral 1 over open parentheses 2 x close parentheses to the power of begin display style 1 third end style end exponent d x end cell row blank equals cell 2 over 3 integral fraction numerator 1 over denominator 2 to the power of begin display style 1 third end style end exponent times x to the power of begin display style 1 third end style end exponent end fraction d x end cell row blank equals cell 2 over 3 times 1 over 2 to the power of begin display style 1 third end style end exponent integral 1 over x to the power of 1 third end exponent d x end cell row blank equals cell 2 over 3 times 1 over 2 to the power of begin display style 1 third end style end exponent times integral x to the power of negative 1 third end exponent d x plus straight C end cell row blank equals cell 2 to the power of begin display style 2 over 3 end style end exponent over 3 times fraction numerator 1 over denominator negative begin display style 1 third end style plus 1 end fraction x to the power of negative 1 third plus 1 end exponent plus straight C end cell row blank equals cell 2 to the power of begin display style 2 over 3 end style end exponent over 3 times fraction numerator 1 over denominator begin display style 2 over 3 end style end fraction straight x to the power of 2 over 3 end exponent plus straight C end cell row blank equals cell fraction numerator cube root of 4 over denominator 3 end fraction times 3 over 2 straight x to the power of 2 over 3 end exponent plus straight C end cell row blank equals cell fraction numerator cube root of 4 over denominator 3 end fraction times fraction numerator 3 cube root of x squared end root over denominator 2 end fraction plus straight C end cell row blank equals cell cube root of 4 times fraction numerator cube root of x squared end root over denominator 2 end fraction plus straight C end cell row blank equals cell fraction numerator cube root of 4 x squared end root over denominator 2 end fraction plus straight C end cell end table

Maka, hasil dari integral fraction numerator 2 over denominator 3 cube root of 2 x end root end fraction d x equals fraction numerator cube root of 4 x squared end root over denominator 2 end fraction plus straight C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juli 2021

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