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

[Jeann25]

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

 

[EbolaPox]

$$\int {\sqrt{sin(x)}} cos(x)^3 dx$$

Convert this into

$$\int {\sqrt{sin(x)}}cos^2(x)cos(x)$$.

From your identities in trignometry

$$cos^2(x) = 1 - sin^2(x)$$.

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?

 

[Jeann25]

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

 

[d_leet]

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.