Question

Evaluate :-
integrate cos³x . dx​

Answer 1

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