Integrate 1 3 &#xFEFF; </mrow> t 4 </mrow> tan

Aedan Gonzales

Aedan Gonzales

Answered question

2022-05-13

Integrate 1 3  t 4 tan ( 5 t 5 ) sec ( 5 t 5 ) with respect to t.

Answer & Explanation

Finnegan Zimmerman

Finnegan Zimmerman

Beginner2022-05-14Added 16 answers

Simplify.

tan(5t5)t4sec(5t5)3dt

Since 13 is constant with respect to t, move 13 out of the integral.

13tan(5t5)t4sec(5t5)dt

Let u=5t5. Then du=25t4dt, so 125du=t4dt. Rewrite using u and du.

13tan(u)sec(u)125du

Simplify.

13tan(u)sec(u)25du

Since 125 is constant with respect to u, move 125 out of the integral.

13(125tan(u)sec(u)du)

Simplify.

175tan(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).

175(sec(u)+C)

Simplify.

175sec(u)+C

Replace all occurrences of u with 5t5.

175sec(5t5)+C

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