Can the Indefinite Integral of sqrt(2x+1)dx be Expressed as 1/3(2x+1)^3/2 + C?

[sapiental]

evaluate the indefinite integral sqrt(2x+1)dx

I let u^2 = 2x+1

then

indefinite integral u^2du

1/3u^3 + C

1/3(sqrt(2x+1))^3 + C is my finals answer

can this also be written like this 1/3(2x+1)^3/2 + C?


Thanks

 

[stunner5000pt]

yes you are correct

 

[quasar987]

Your answer is right, but I have no idea what you just did. Would you mind explaining it to me?

 

[sapiental]

sure,

I skipped a few steps in my previous post.

evaluate the indefinite integral sqrt(2x+1)dx

u = sqrt(2x+1)

du = dx/sqrt(2x+1)

sqrt(2x+1)du = dx

or

udu = dx

rewriting the integral

indefinite integral u x udu

= indefinite integral u^2du

then just take antiderivative of u^2 and substitute sqrt(2x+1) back into it

 

[quasar987]

oooh, I see now, thx!

 

[HallsofIvy]

Probably Quasar987 was used the substitution u= 2x+1 which gives the same answer.