Question

Find the integral:
∫√(6x-7) dx

Please would like to know an explanation...
I will appreciate, thanks!! ;)

Answer 1

a simple u-substitution will do the trick: u = 6x-7, so du = 6dx

try that....

Answer 2

Please help me, to get into the answer.. I will appreciate. Thanks!

Answer 3

use dpaInc's hint to go from

∫√(6x-7) dx

to

(1/6)*∫√u du

Answer 4

when you substitute u and du into the equation you will go from
\[\int\limits_{}^{} (\sqrt{6x-7}dx\]
to
\[\int\limits_{}^{}\sqrt{u} \frac{ du }{ 6 }\]

because
{u = 6x-7}
and
{du = 6dx}
so divide both sides by 6 and you will be able to substitute for dx... (du/6)

Once you understand that..
integrate the equation and you will get,
\[\frac{ 2u ^{3/2} }{ 3 } (\frac{ 1 }{ 6 })\]

Substitute u back into the equation
you will get...

\[\frac{ 2(6x-7)^{3/2} }{ 3 }(\frac{ 1 }{ 6 })\]

Solved.

Answer 5

@rocal2

Answer 6

Sorry I forgot one part, add +C to the end of your answer for your constant after integrating.

Answer 7

Thanks!! I like it, I will try another one....

Answer 8

Your Welcome