Compute 2 <mrow> 3 t ln &#x2061;<!-- ⁡ 4

bedblogi38am

bedblogi38am

Answered question

2022-05-11

Compute 2 3 t ( ln ( 4 t ) 1 )  d t.

Answer & Explanation

necrologo9yh43

necrologo9yh43

Beginner2022-05-12Added 23 answers

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

231t(ln(4t)-1)dt

Let u2=ln(4t). Then du2=1tdt, so tdu2=dt. Rewrite using u2 and du2.

231u2-1du2

Let u3=u2-1. Then du3=du2. Rewrite using u3 and du3.

231u3du3

The integral of 1u3 with respect to u3 is ln(|u3|).

23(ln(|u3|)+C)

Simplify.

23ln(|u3|)+C

Substitute back in for each integration substitution variable.

23ln(|(4t)-1|)+C

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