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March 29, 2017

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FIND EACH INDEFINITE INTERGRAL BY THE SUBSTITUTION METHOD

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

  • CALCULUS - ,

    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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