Integral of ∫ tan 5 ⁡ ( x ) sec 4 ⁡ ( x )...

Theresa Archer

Theresa Archer

Answered

2022-06-26

Integral of tan 5 ( x ) sec 4 ( x ) d x?

Answer & Explanation

Jaylee Dodson

Jaylee Dodson

Expert

2022-06-27Added 22 answers

Substituting u = tan ( x ) , d u = sec 2 ( x ) d x
tan 5 ( x ) sec 4 ( x ) d x = tan 5 ( x ) sec 2 ( x ) sec 2 ( x ) d x = tan 5 ( x ) [ tan 2 ( x ) + 1 ] sec 2 ( x ) d x = u 5 ( u 2 + 1 ) d u = u 7 + u 5 d u = 1 8 u 8 + 1 6 u 6 + c = 1 8 tan 8 ( x ) + 1 6 tan 6 ( x ) + c

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