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Math Help - Find antiderivative here

  1. #1
    Newbie Critter314's Avatar
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    Find antiderivative here

    Is antiderivative of (6x^2+1) is it 2x^3+x+C?
    Is antiderivative of \frac{1}{4z} is it \frac{1}{4}\ln4z+C?
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Critter314 View Post
    Is antiderivative of (6x^2+1) is it 2x^3+x+C?
    Yes (Clap)

    Is antiderivative of \frac{1}{4z} is it \frac{1}{4}\ln4z+C?
    Yes (Clap)
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  3. #3
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    Hello, Critter314!

    \text{The antiderivative of }\,\dfrac{1}{4z}

    \text{Is it }\,\frac{1}{4}\ln4z+C\,?

    Well, yes and no . . .


    Note that: . \displaystyle \int\frac{dz}{4z} \;=\;\tfrac{1}{4}\int\frac{dz}{z} \;=\; \tfrac{1}{4}\ln z + C


    Your answer is correct, but it can be simplified.

    . . \frac{1}{4}\ln4z + C \;=\; \frac{1}{4}\bigg[\log 4 + \ln z\bigg] + C

    . . . . . . . . . . . =\;\underbrace{\tfrac{1}{4}\ln4}_{\text{constant}} + \frac{1}{4}\ln z + C

    . . . . . . . . . . . =\;\tfrac{1}{4}\ln z + C

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