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    I'm unsure on how I'd integrate 6sin(x)cos^3(x)?
    Thanks
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    You don't have to use substitution to integrate that. See what happens when you differentiate cos^4(x), it should be something very similar.
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    By substitution:

    Let u = cosx. When you find dx you'll see why this is nice.


    Alternatively, you don't need a substitution. Notice that sin is the differential of cos. Try raising the power of cos to 4 and see what you need to put in front and check it by differentiating your answer. (it'll produce a sin)
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    (Original post by Grewsters)
    I'm unsure on how I'd integrate 6sin(x)cos^3(x)?
    Thanks
    I would write cos^3(X)=cos(X)*cos^2(X) and sub cos^2(X)=\frac{1+cos(2x)}{2} and go from there
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    (Original post by JamesN111)
    You don't have to use substitution to integrate that. See what happens when you differentiate cos^4(x), it should be something very similar.
    (Original post by AmarPatel98)
    By substitution:

    Let u = cosx. When you find dx you'll see why this is nice.


    Alternatively, you don't need a substitution. Notice that sin is the differential of cos. Try raising the power of cos to 4 and see what you need to put in front and check it by differentiating your answer. (it'll produce a sin)
    (Original post by Aph)
    I would write cos^3(X)=cos(X)*cos^2(X) and sub cos^2(X)=\frac{1+cos(2x)}{2} and go from there
    Thank you!
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    (Original post by AmarPatel98)
    By substitution:

    Let u = cosx. When you find dx you'll see why this is nice.


    Alternatively, you don't need a substitution. Notice that sin is the differential of cos. Try raising the power of cos to 4 and see what you need to put in front and check it by differentiating your answer. (it'll produce a sin)
    Or use d1 flowcharts
 
 
 

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