Integrate 8 7 x 3 </mrow> tan &#x2061;<!-- ⁡

deformere692qr

deformere692qr

Answered question

2022-04-10

Integrate 8 7 x 3 tan ( x 4 + 4 ) sec ( x 4 + 4 ) with respect to x.

Answer & Explanation

Lankenp19hh

Lankenp19hh

Beginner2022-04-11Added 11 answers

Simplify.

tan(x4+4)(8x3)sec(x4+4)3dx

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

83tan(x4+4)(x3)sec(x4+4)dx

Let u=x4+4. Then du=4x3dx, so 14du=x3dx. Rewrite using u and du.

83tan(u)sec(u)14du

Simplify.

83tan(u)sec(u)4du

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

83(14tan(u)sec(u)du)

Simplify.

23tan(u)sec(u)du

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

23(sec(u)+C)

Simplify.

23sec(u)+C

Replace all occurrences of u with x4+4.

23sec(x4+4)+C

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