# Calculus (Antiderivatives)

posted by Mishaka

What is the antiderivative of the following expression?
3x(x^2 + 7)^3

1. Steve

hard way: expand the product:
3x^7 + 63x^5 + 441x^3 + 1029x
integral is
3/8 x^8 + 21/2 x^6 + 441/4 x^4 + 1029/2 x^2

easy way: let u = x^2+7
du = 2x dx
Integral of 3/2 u^3 du
is
3/8 u^4 = 3/8 (x^2+7)^4

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