Integral x √1+x^2 dx

integral substitusi

∫ x √(1+x²) dx = ∫ x (1+x²)¹/²

u = 1 + x²
du = 2x dx --> x. dx = ¹/₂ du

∫ x (1+x²)¹/² dx = ¹/₂  ∫ u¹/²du =¹/₂.²/₃. u³/² + c
= ¹/₃ u√ u + c
= ¹/₃  (1 + x²) √(1+x²) + c