Evaluate :-
integrate cos³x . dx
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Answer:
ok ok
Step-by-step explanation:
Method 1:
∫cos3x dx
=∫cosx(cos2x) dx
=∫cosx(1−sin2x) dx
=∫cosx dx−∫sin2xcosx dx
=sinx−∫(sinx)2 d(sinx)
=sinx−(sinx)33+C
=sinx−sin3x3+C
Method 2: we know that cos3x=4cos3x−3cosx⟹cos3x=3cosx+cos3x4
∴∫cos3x dx
=∫(3cosx+cos3x4) dx
I hope helpful to you
=∫3cosx dx+∫cos3x4 dx
=34∫cosx dx+14⋅13∫cos3x d(3x)
=34sinx+112sin3x+C
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