Evaluate ∫ cos(3 x + 2 ) dx.

Question 17

EasyOriginal question

Evaluate $\int \cos{\left(3 x + 2 \right)}\,dx$ .

\frac{\sin{\left(3 x + 2 \right)}}{3} + C

Correct answerYour answer

\sin{\left(3 x + 2 \right)} + C

Correct answerYour answer

- \frac{\sin{\left(3 x + 2 \right)}}{3} + C

Correct answerYour answer

x \cos{\left(3 x + 2 \right)} + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Put $t = 3x + 2$ ; then $dt$ is the rest of the integrand, up to a constant.
The integral becomes a standard form in $t$ ; putting $t = 3x + 2$ back gives $\frac{\sin{\left(3 x + 2 \right)}}{3} + C$ .
Check: differentiating the answer gives back the integrand.

Worth noting

Getting the constant from $dt$ wrong multiplies or divides the answer: check by differentiating.

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