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- King LeoLv 74 years agoFavorite Answer
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let u = x² + 3 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯➤ du/dx = 2x ⎯⎯⎯⎯⎯⎯⎯⎯➤ dx = du/(2x)
y = ∫ 12x(x² + 3)⁵ dx
y = ∫ 12x ( u )⁵ dx
y = ∫ 12x ( u )⁵ * du/(2x)
y = ∫ 6 u⁵ du
y = u⁶ + C
y = (x² + 3)⁶ + C
3 = (6² + 3)⁶ + C
C = -3518743758
- SqdancefanLv 74 years ago
∫12x(x^2 +3)^5·dx = (x^2 +3)^6 +c
At x=6, you want
.. 3 = (6^2 +3)^6 +c
.. 3 = 39^6 +c
.. c = 3 - 39^6
.. c = -3,518,743,758
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