Find the integral: <mrow> 2 tan &#x2061;<!-- ⁡ ln &

zuzogiecwu

zuzogiecwu

Answered question

2022-05-11

Find the integral: 2 tan ( ln ( 2 x ) + 6 ) sec ( ln ( 2 x ) + 6 ) 3 x  d x.

Answer & Explanation

Mackenzie Zimmerman

Mackenzie Zimmerman

Beginner2022-05-12Added 15 answers

Since 23 is constant with respect to x, move 23 out of the integral.

23tan(ln(2x)+6)sec(ln(2x)+6)xdx

Let u2=ln(2x)+6. Then du2=1xdx, so xdu2=dx. Rewrite using u2 and du2.

23tan(u2)sec(u2)du2

Since the derivative of sec(u2) is tan(u2)sec(u2), the integral of tan(u2)sec(u2) is sec(u2).

23(sec(u2)+C)

Simplify.

23sec(u2)+C

Replace all occurrences of u2 with ln(2x)+6.

23sec(ln(2x)+6)+C

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?