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Verified answer
InTegraLMisal :
u = 3x² + 1
du/dx = 6x
2 . 3x dx = du
3x dx = 1/2 du
•••
∫3x √(3x² + 1) dx
= 1/2 ∫ u^1/2 du
= 1/2 . 1/(3/2) . u^3/2 + C
= 1/3 . (3x² + 1)√(3x² + 1) + C