U-Substitution

[odd monolith]

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[trail hawk]

recall the derivative of exponential functions..

$\dv{x}a^x=\dv{x}e^{\ln(a)x}=\ln(a)e^{\ln(a)x}=a^x\ln(a)$

[grizzled portal]

Omegabet_

[grim iris]

Using this, I get to the point where du = (3^x)(ln3)(dx) but then how does that factor into making the function just u's? (3^x)(ln3) isn't anywhere in the question I don't think.

[trail hawk]

$u=3^x+4\implies\dd{u}=3^x\ln(3)\dd{x}\implies\int\frac{3^x}{\sqrt{3^x+4}}\dd{x}=\int\frac{1}{\sqrt{u}}\frac{1}{\ln(3)}\dd{u}$

[grizzled portal]

Omegabet_

[grim iris]

I get it now. Thanks for the help.

[viscid bloom]

Rep Confirmation

Award @trail hawk with reputation points?

[grim iris]

+close

[odd monolith]

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