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Pertanyaan

Nilai ∫ x ​ ( 2 3 ​ 3 x ​ + 3 ) dx= …

Nilai   

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H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai

nilai integral square root of x open parentheses 3 over 2 cube root of x plus 3 close parentheses space d x equals 9 over 11 x root index 6 of x to the power of 5 end root plus 2 x square root of x plus c 

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Pembahasan

Nilai integral tersebut adalah sebagai berikut. Dengan demikian, nilai

Nilai integral tersebut adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral square root of x open parentheses 3 over 2 cube root of x plus 3 close parentheses space d x end cell row blank equals cell integral x to the power of 1 half end exponent open parentheses 3 over 2 x to the power of 1 third end exponent plus 3 close parentheses d x end cell row blank equals cell integral open parentheses 3 over 2 x to the power of 1 half plus 1 third end exponent plus 3 x to the power of 1 half end exponent close parentheses d x end cell row blank equals cell integral open parentheses 3 over 2 x to the power of 5 over 6 end exponent plus 3 x to the power of 1 half end exponent close parentheses d x end cell row blank equals cell 3 over 2 times 6 over 11 x to the power of 11 over 6 end exponent plus 3 times 2 over 3 x to the power of 3 over 2 end exponent plus c end cell row blank equals cell 9 over 11 x root index 6 of x to the power of 5 end root plus 2 x square root of x plus c end cell end table

Dengan demikian, nilai integral square root of x open parentheses 3 over 2 cube root of x plus 3 close parentheses space d x equals 9 over 11 x root index 6 of x to the power of 5 end root plus 2 x square root of x plus c 

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