Differentiation by parts

[pearl ether]

Can someone guide me through this differentiation by parts, imhaving troubtrouble understand it

[steady walrus]

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[inland wagon]

why did they not provide the method.

anyways, here v= 4(ln(3t)) and du=ln(3t)

wait what?

thats incorrect

holy crap

unless they skipped the first IBP

here let me show you a different and more accurate way

let v=4(ln(3t)^2) and du=1

then dv=8(ln(3t))*1/t and du=t

thus we have $4t(\ln(3t))^2-\int 8\ln(3t) dt$

[lime mesa]

;( | 追放された興奮

[inland wagon]

let u=3t, then du=3dt

thus we have $4t(ln(3t))^2-\frac{8}{3}\int\ln(u)du$

[lime mesa]

;( | 追放された興奮

[inland wagon]

therefore we have $4t(ln(3t))^2-\frac{8}{3}(u\ln(u)-u)$

[lime mesa]

;( | 追放された興奮

[inland wagon]

and you can solve from here

[pearl ether]

damn that makes sm sense compared to the answer they gave

[pearl ether]

ty sm

[nocturne glen]

@pearl ether has given 1 rep to @inland wagon

[pearl ether]

+close