Integrating (4x+1)^1/2 | Homework Help

[Priyadarshini]

Homework Statement

Integrate (4x+1)^1/2

Homework Equations

Integration (ax+b)^n dx= (ax+b)^(n+1)/ a(n+1)

The Attempt at a Solution

(4x+1)^(3/2)/ 4(3/2)
= (4x+1)^(3/2)/6

but the actual answer is
3(4x+1)^(3/2)/8

 

[SammyS]

Homework Statement

Integrate (4x+1)^1/2

Homework Equations

Integration (ax+b)^n dx= (ax+b)^(n+1)/ a(n+1)

The Attempt at a Solution

(4x+1)^(3/2)/ 4(3/2)
= (4x+1)^(3/2)/6

but the actual answer is
3(4x+1)^(3/2)/8

Take the derivative of your result and the correct result. Compare to help you see where you went awry .

 

[Ray Vickson]

Homework Statement

Integrate (4x+1)^1/2

Homework Equations

Integration (ax+b)^n dx= (ax+b)^(n+1)/ a(n+1)

The Attempt at a Solution

(4x+1)^(3/2)/ 4(3/2)
= (4x+1)^(3/2)/6

but the actual answer is
3(4x+1)^(3/2)/8

No, the actual answer is what YOU obtained. Try differentiating your answer, to check if you get back your initial $(4x+1)^{1/2}$.

 

[ehild]

The Attempt at a Solution

(4x+1)^(3/2)/ 4(3/2)
= (4x+1)^(3/2)/6

Your result is correct. (but do not forget adding a C constant )

 

[Priyadarshini]

No, the actual answer is what YOU obtained. Try differentiating your answer, to check if you get back your initial $(4x+1)^{1/2}$.

It does. Thank you!

 

[Priyadarshini]

Your result is correct. (but do not forget adding a C constant )

I keep forgetting to add the constant! Thanks!