Anti-derivative question calculus?

Hi I am stuck on this problem and need some guided help. I know one is usually added to the exponent to the numerator and denominator , but after that I am confused on this one. The answer was (2X - 3)^[5]/[10] + C .

The problem : Evaluate the antiderivative ---> (curved S sign I don't know how to represent but its antiderivative of (2x - 3) ^ 4 dx

Here's the link if someone does not get my notation :http://www.baruch.cuny.edu/sacc/documents/MTH2205_... problem A14

3 Answers

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  • 8 years ago
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    You can definitely use a substitution.

    ∫(2x - 3)^4 dx

    z = 2x - 3 => dz/2 = dx

    1/2*∫z^4 dz = 1/10 * z^5 + C

    = 1/10 * (2x - 3)^5 + C

  • 8 years ago

    ∫ (2x - 3)^4dx

    let u = 2x - 3

    du = 2dx

    =1/2∫u^4du

    =1/10u^5 + C

    substitute back for u = 2x - 3

    =1/10(2x - 3)^5 + C answer//

  • 8 years ago

    I can't answer, only assist. You will end up with 2 possible answers though, the more obvious of the 2 being the derivative, the other being the anti-derivative. Sorry I can't be more help though

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