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C4 Integration HELP!

Hi,

I'm finding it difficult to integrate the following, and was hoping someone could show me how to do it in the quickest method possible:

∫ (cosx+secx)² dx

Answer: 5/2x + 1/4sin2x + tanx

Thank you very much! :smile:
sweet_gurl
Hi,

I'm finding it difficult to integrate the following, and was hoping someone could show me how to do it in the quickest method possible:

∫ (cosx+secx)² dx

Answer: 5/2x + 1/4sin2x + tanx

Thank you very much! :smile:

expand brackets.

cos^2x + 2cosx.secx + sec^2x
= 0.5 + 0.5cos2x + 2 + sec^2x
= 5/2 + 0.5cos2x + sec^2x

Integral gives
5x/2 + 0.25sin2x + tanx + c
Reply 2
Avatar for sweet_gurl
sweet_gurl
OP
4
I can see what you've done, but I'm not sure how to get
0.5 + 0.5cos2x + 2 + sec^2x from cos^2x + 2cosx.secx + sec^2x
sweet_gurl
I can see what you've done, but I'm not sure how to get
0.5 + 0.5cos2x + 2 + sec^2x from cos^2x + 2cosx.secx + sec^2x


cos2x = cos^2x - sin^2x (double angle)
cos2x = 2cos^2x - 1 (sin^2x = 1-cos^2x)

=> cos^2x = 1/2 + 1/2cos2x

2cosx.secx = 2 x cosx x 1/cosx = 2cosx/cosx = 2
Reply 4
Avatar for sweet_gurl
sweet_gurl
OP
4
Widowmaker
cos2x = cos^2x - sin^2x (double angle)
cos2x = 2cos^2x - 1 (sin^2x = 1-cos^2x)

=> cos^2x = 1/2 + 1/2cos2x

2cosx.secx = 2 x cosx x 1/cosx = 2cosx/cosx = 2



Thank you! :smile:

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