Find the integral of 6 7 </mfrac> <mrow class="MJX-TeXAtom-ORD"> &#xFEFF; </mr

Araceli Soto

Araceli Soto

Answered question

2022-04-30

Find the integral of 6 7  cos ( 3 5 x ) with respect to x.

Answer & Explanation

catcher1307ieh

catcher1307ieh

Beginner2022-05-01Added 15 answers

Since 6 7 is constant with respect to x, move 6 7 out of the integral.
6 7 cos ( 3 5 x ) d x
Let u=3-5x. Then du=-5dx, so 1 5 d u = d x. Rewrite using u and du
6 7 cos ( u ) 1 5 d u
Simplify
6 7 cos ( u ) 5 d u
Since -1 is constant with respect to u, move -1 out of the integral.
6 7 ( cos ( u ) 5 d u )
Since 1 5 is constant with respect to u, move 1 5 out of the integral.
6 7 ( ( 1 5 cos ( u ) d u ) )
Simplify
6 35 cos ( u ) d u
The integral of cos ( u ) with respect to u is sin ( u )
6 35 ( sin ( u ) + C )
Simplify
6 35 sin ( u ) + C
Replace all occurrences of u with 3-5x.
6 35 sin ( 3 5 x ) + C

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