# CALCULUS

posted by renee

FIND EACH INDEFINITE INTERGRAL BY THE SUBSTITUTION METHOD

(X^4-16)^5 X^3 DX

1. MathMate

Hint:
note the x^4 in parentheses, and that d(x^4)/dx = 4x^3, so substituting
y=x^4 would have a good chance of success.
If
y=x^4-16,
dy=4x^3dx

So
I=∫(X^4-16)^5 X^3 DX
=∫y^5(dy/4)
proceed with the power rule and put back y=x^4-16 into I.
Do not forget the integration constant C.

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