integral3x(x^2+7)^5dx

InTegraL

∫ax^n dx = a/(n+1) . x^(n+1) + C

Misal :
u = x² + 7
du/dx = 2x
2x dx = du
3 . 2x dx = 3 du
3x dx = 3/2 du

••
∫3x (x² + 7)^5 dx
= ∫u^5 . 3/2 du
= 3/2 ∫u^5 du
= 3/2 . 1/6 u^6 + C
= 1/4 (x² + 7)^6 + C ✔