Evaluate 8 3 &#xFEFF; </mrow> tan &#x2061;<!-- ⁡ 4 t <mo st

Noelle Wright

Noelle Wright

Answered question

2022-04-10

Evaluate 8 3  tan ( 4 t ) e sec ( 4 t ) sec ( 4 t ) d t.

Answer & Explanation

Cecelia Mullins

Cecelia Mullins

Beginner2022-04-11Added 10 answers

Simplify.

8esec(4t)tan(4t)sec(4t)3dt

Since 83 is constant with respect to t, move 83 out of the integral.

83esec(4t)tan(4t)sec(4t)dt

Let u2=sec(4t). Then du2=4sec(4t)tan(4t)dt, so 14du2=sec(4t)tan(4t)dt. Rewrite using u2 and du2.

83eu214du2

Combine eu2 and 14.

83eu24du2

Since 14 is constant with respect to u2, move 14 out of the integral.

83(14eu2du2)

Simplify.

23eu2du2

The integral of 2eu2 with respect to u2 is eu2.

23(eu2+C)

Simplify.

23eu2+C

Replace all occurrences of u2 with sec(4t).

23esec(4t)+C

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