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Numerade Educator

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Problem 4 Medium Difficulty

Verify by differentiation that the formula is correct.

$ \displaystyle \int x\sqrt{a + bx} \,dx = \frac{2}{15b^2}(3bx - 2a)(a + bx)^{3/2} + C $

Answer

$\frac{2}{3 b^{2}}(b x-2 a) \sqrt{a+b x}+C$

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Video Transcript

okay. Using the product rule weaken drive after promise acts to be too over three b squared times G prime of acts times h of acts pushed g of x times. So now that we have this recall the fact that G prime vexes B and then we know we also h promise tax. Therefore, what we have is the integral of acts over sward of a plus. P axe is to over three b square, which is this part over here you can see familiar times B X minus Julia times a plus B ox plus C.