Integral by use of substitution (int 3cos x dx)/(sqrt(1+3sin x))

Deromediqm 2022-07-30 Answered
Integral by use of substitution 3 cos x d x 1 + 3 sin x
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Answers (2)

Eve Good
Answered 2022-07-31 Author has 18 answers
3 cos ( x ) d x 1 + 3 sin ( x )
Note that the derivative of 3 sin ( x ) + 1 is present [ 3 cos ( x ) ], so we can try to use u-substitution.
u = 1 + 3 sin ( x ) what's inside the
d u = 3 cos ( x ) d x precisely our numerator
After substitution, we have
3 cos ( x ) d x 1 + 3 sin ( x ) = 1 u d u
3 cos ( x ) d x 1 + 3 sin ( x ) = u 1 2 d u
Integrating
3 cos ( x ) d x 1 + 3 sin ( x ) = 2 u 1 2 + C
3 cos ( x ) d x 1 + 3 sin ( x ) = 2 u + C
Writing in terms of x
3 cos ( x ) d x 1 + 3 sin ( x ) = 2 1 + 3 sin ( x ) + C
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agantisbz
Answered 2022-08-01 Author has 2 answers
3 cos x 1 + 3 sin x d x = 1 u d u
take u = 1 + 3 sin x
d u = 3 cos x d x = u 1 / 2 d u = u 1 / 2 + c = 1 + 3 sin x + c
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