Bagaimana penyelesaian dari integral tan^6 2x dx

Integral^6 2x dx
Misal
u = 2x
du = 2 dx
Integral tan^6 2x
= ½ integral tan^6 u du
= ½ (integral tan⁴u (sec²u -1) du)
= ½ (integral tan⁴u sec²u du - integral tan⁴u du)
= ½ (1/5 tan^5 u + K - integral tan²u (sec²u- 1) du)
= ½ (1/5 tan^5 u + K - Integral tan²u sec²u du+ integral tan² u du)
= ½ (1/5 tan^5 u + K - ⅓ tan³u + L + integral (sec²u -1) du)
= ½ (1/5 tan^5 u - ⅓ tan³u + M + tan u - u + N)
= ½ (1/5 tan^u - ⅓tan³ u + tan u - u + P)
= 1/10 tan^5 2x - 1/6tan³2x + tan2x - 2x + C


Keterangan
Integral tan²u sec² u du
Misal n = tan u
dn = sec²u du
Maka integral tan²u sec²u du
=integral n²dn
= ⅓n³ + C
= ⅓tan³u + C