Indefinate Integral Queston. (1 Viewer)

[Muz4PM]

Hello, I would appreciate it if some people could assist me with some Indefinate Integrals. I get some parts of them, but I am unable to bring them completely together. The questions I am stuck on are:

(sign thing) x . (2x+7)^1/2 dx

Substitute
a) u = 2x + 7
b) u^2 = 2x + 7

Any assistance would be appreciated. Thanks.

 

[Trebla]

a) u = 2x + 7
=> x = (u - 7) / 2
=> du = 2.dx
∫x.(2x + 7)^1/2 dx
=∫u^1/2 (u - 7) / 4 du
=∫(u^3/2 - 7u^1/2) / 4 du
= 2u^5/2 / 20 - 14u^3/2 / 12 + c
= 2(2x + 7)^5/2 / 20 - 14(2x + 7)^3/2 / 12 + c
= (2x + 7)^5/2 / 10 - 7(2x + 7)^3/2 / 6 + c

b) u² = 2x + 7
=> u = (2x + 7)^1/2
=> x = (u² - 7) / 2
=> dx = u.du
∫x.(2x + 7)^1/2dx
=∫u² (u² - 7) / 2 du
=∫(u⁴ - 7u²) / 2 du
= u⁵ / 10 - 7u³ / 6 + c
= (2x + 7)^5/2 / 10 - 7(2x + 7)^3/2 / 6 + c

 

[davidbarnes]

I too got stuck on that same question today. If you are still stuck I can post my solution if you want.

 

[Muz4PM]

I get it now, thank you for your explaination Trebla, it is much appreciated. David Barnes, thank you for your kind offer, but it would not be neccessary as I now grasp the concept. Thanks to the both of you.

 

[Caitlin63]

ooh yes thanks Trebla I got stuck with this one too but I now understand the point really well! Thanks!