Compute 3 4 &#xFEFF; </mrow> e tan &#x2061;<!-- ⁡

Landon Mckinney

Landon Mckinney

Answered question

2022-05-12

Compute 3 4  e tan ( 6 x ) sec 2 ( 6 x ) d x.

Answer & Explanation

Juliet Mcdonald

Juliet Mcdonald

Beginner2022-05-13Added 15 answers

Simplify.

3etan(6x)sec2(6x)4dx

Since 34 is constant with respect to x, move 34 out of the integral.

34etan(6x)sec2(6x)dx

Let u2=tan(6x). Then du2=6sec2(6x)dx, so 16du2=sec2(6x)dx. Rewrite using u2 and du2.

34eu216du2

Combine eu2 and 16.

34eu26du2

Since 16 is constant with respect to u2, move 16 out of the integral.

34(16eu2du2)

Simplify.

18eu2du2

The integral of eu2 with respect to u2 is eu2.

18(eu2+C)

Simplify.

18eu2+C

Replace all occurrences of u2 with tan(6x).

18etan(6x)+C

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