Integrating sqroot(kx + (1/4)(k^2)) using basic integration techniques

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In summary, the formula for integrating sqroot(kx + (1/4)(k^2)) using basic integration techniques is: ∫√(kx + (1/4)(k^2)) dx = (2/3k)(kx + (1/4)(k^2))^3/2 + C. The basic integration techniques used to solve sqroot(kx + (1/4)(k^2)) are substitution, integration by parts, and trigonometric substitution. Yes, sqroot(kx + (1/4)(k^2)) can be solved using u-substitution. The power rule for integration states that ∫x^n dx = (1/(n+1))x
  • #1
meee
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help me integrate this please

sqroot( kx + (1/4)(k^2) ) dx

i wud like to know whether its solvable? and how to do it?
 
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  • #2
So your k is a constant right?
To do this kind of problem, we usually use the u-substitution:
u = kx + 1 / 4 k2
Ok, can you go from here? :)
 
  • #3
ok thanks... yes k = constant

2/(3k) * (kx + (1 / 4) k^2 ) ^(3/2)
is that right?
 
  • #4
You are forgetting the Constant of Integration. :)
Everything else is correct.
 
  • #5
oh yes thanks
 

Related to Integrating sqroot(kx + (1/4)(k^2)) using basic integration techniques

What is the formula for integrating sqroot(kx + (1/4)(k^2)) using basic integration techniques?

The formula for integrating sqroot(kx + (1/4)(k^2)) using basic integration techniques is: ∫√(kx + (1/4)(k^2)) dx = (2/3k)(kx + (1/4)(k^2))^3/2 + C

What are the basic integration techniques used to solve sqroot(kx + (1/4)(k^2))?

The basic integration techniques used to solve sqroot(kx + (1/4)(k^2)) are substitution, integration by parts, and trigonometric substitution.

Can sqroot(kx + (1/4)(k^2)) be solved using u-substitution?

Yes, sqroot(kx + (1/4)(k^2)) can be solved using u-substitution. In this case, u = kx + (1/4)(k^2) and du = kdx.

What is the power rule for integration?

The power rule for integration states that ∫x^n dx = (1/(n+1))x^(n+1) + C, where n is any real number except -1.

Can trigonometric substitution be used to solve sqroot(kx + (1/4)(k^2))?

Yes, trigonometric substitution can be used to solve sqroot(kx + (1/4)(k^2)) by using the substitution u = √(kx + (1/4)(k^2)) and then applying the appropriate trigonometric identities to simplify the integral.

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