Evaluate 4 9 &#xFEFF; </mrow> e 6 x </mrow>

Micah Haynes

Micah Haynes

Answered question

2022-04-10

Evaluate 4 9  e 6 x tan ( e 6 x + 4 ) sec ( e 6 x + 4 ) d x.

Answer & Explanation

hi3c4a2nvrgzb

hi3c4a2nvrgzb

Beginner2022-04-11Added 15 answers

Simplify.

tan(e6x+4)(4e6x)sec(e6x+4)9dx

Since 49 is constant with respect to x, move 49 out of the integral.

49tan(e6x+4)(e6x)sec(e6x+4)dx

Let u2=e6x+4. Then du2=6e6xdx, so 16du2=e6xdx. Rewrite using u2 and du2.

49tan(u2)sec(u2)16du2

Simplify.

49tan(u2)sec(u2)6du2

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

49(16tan(u2)sec(u2)du2)

Simplify.

227tan(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).

227(sec(u2)+C)

Simplify.

227sec(u2)+C

Replace all occurrences of u2 with e6x+4.

227sec(e6x+4)+C

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