integral 1/3x✓x dx

Hai, kakak bantu jawab yah! Jawabanya: -2/(3√x) +C Ingat! 1) Aturan integral ∫axⁿ dx = a/(n+1) xⁿ⁺¹ +c 2) Aturan bentuk pangkat! √x=x^1/2 1/(x^n)=x^(-n) Diasumsikan soalnya adalah ∫1/(3x√x) dx sehingga diperoleh: ∫1/(3x√x) dx=∫1/(3x·x^(1/2)) dx =∫1/(3x^(1+1/2)) dx =∫1/(3x^(3/2)) dx =∫(x^(-3/2))/3 dx =(x^(-3/2+1))/3(-3/2+1) +C =(x^(-1/2))/3(-1/2) +C =(x^(-1/2))/(-3/2) +C =-2/3(x^(1/2)) +C =-2/(3√x) +C Jadi, ∫1/(3x√x) dx adalah -2/(3√x) +C