Ray10
  • Ray10
can't identify what I'm missing: anti-differentiate 4x*(SQRT)x^2 +3 dx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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.Sam.
  • .Sam.
You mean \[\int\limits 4x \sqrt{x^2+3}dx\]
Ray10
  • Ray10
\[\int\limits_{}^{} 4x \sqrt{x ^{2}+3} dx\]
Ray10
  • Ray10
yup! I've been trying to work it out and it comes to the end but

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.Sam.
  • .Sam.
Have you tried using u-sub \[u=x^2+3\]
Ray10
  • Ray10
yes I subbed that in as u, and got \[\frac{ du }{ dx } = 4x\] the answer is \[\frac{ 4 }{ 3 }(x ^{2}+3)^{\frac{ 3 }{ 2 }}+c\]
Ray10
  • Ray10
when I work it out after coming to the simplified equation of \[\int\limits_{}^{} \sqrt{u} du\]
.Sam.
  • .Sam.
Do it like this, \[u=x^2+3\] \[du=2xdx\] \[\frac{du}{2}=xdx\] ------------------------------------------ \[\int\limits\limits 4x \sqrt{x^2+3}dx\] \[4\int\limits\limits \sqrt{u}\frac{du}{2}\] \[2 \int\limits \sqrt{u}du\]
.Sam.
  • .Sam.
You forgot the 2
Ray10
  • Ray10
oh gosh, I just realized I made \[u = x ^{2} +3 = 4x \] >.<
Ray10
  • Ray10
thank you! so in questions like this remove the constant outside the integral?
anonymous
  • anonymous
yes
Ray10
  • Ray10
ah alright thank you, do I nee to close this question to ask another question or can I just ask it here?
Ray10
  • Ray10
need*

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