Integral of (sin (x))^1/2)(cos^3(x)) dx

  • Thread starter Jeann25
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  • #1
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Not really sure where to begin on this integral. Hope this reads alright on here.

Integral of (sin (x))^1/2)(cos^3(x)) dx
 

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  • #2
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[tex] \int {\sqrt{sin(x)}} cos(x)^3 dx [/tex]

Convert this into

[tex] \int {\sqrt{sin(x)}}cos^2(x)cos(x) [/tex].

From your identities in trignometry

[tex] cos^2(x) = 1 - sin^2(x) [/tex].

This will leave you with all sine terms and one cosine term once you rewrite cosine squared. Do you see what to do from here?
 
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  • #3
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That was very helpful, thank you. Could I also get help with this one pls? :) I just seem to have a hard time figuring out where to start on these.

The integral of (sin(ln x))/x dx
 
  • #4
1,074
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Jeann25 said:
That was very helpful, thank you. Could I also get help with this one pls? :) I just seem to have a hard time figuring out where to start on these.

The integral of (sin(ln x))/x dx
Use a substitution letting u = ln x.
 

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