hasil dari integral x√(x²+5) dx adalah

integral x√(x²+5) dx

Misalkan u = x²+5
    maka  du = 2x dx       ==>   1/2 du = x dx
sehingga integral di atas dapat di tulis

1/2 ∫ √u du
= 1/2 (2/3)u^(3/2) + C
= 1/3 u^(3/2) + C
= 1/3 (x²+5)^(3/2) + C

InTegraL

∫ax^n dx = a/(n+1) . x^(n+1) + C

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Misal :
u = x² + 5
du/dx = 2x
x dx = 1/2 du

∫x√(x² + 5) dx
= ∫u^1/2 . 1/2 du
= 1/2 . 1/(3/2) . u^3/2 + C
= 1/3 u√u + C
= 1/3 (x² + 5)√(x² + 5) + C