1 Answer

Suhprano · Answer 1 · 2022-12-27T07:31:38+0000

Answer:

$I = (1)/(6)\cdot \sin^(2) 3x + C$

Where
is the integration constant.

Explanation:

We use integration by substitution to obtain the integral, where:

$u = \sin 3x$ ,
$du = 3\cdot \cos 3x\,dx$

$I = \int {\sin 3x\cdot \cos 3x} \, dx$

$I = (1)/(3) \int {u} \, du$

$I = (1)/(6)\cdot u^(2) + C$

$I = (1)/(6)\cdot \sin^(2) 3x + C$

Where
is the integration constant.

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