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

- Thread starter Jeann25
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- #1

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

- #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?

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?

Last edited:

- #3

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The integral of (sin(ln x))/x dx

- #4

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Use a substitution letting u = ln x.Jeann25 said:

The integral of (sin(ln x))/x dx

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