Question

integration of secpower4

Answer 1

sec^4x = sec^2x(1 + tan^2x)

= sec^2x + sec^2xtan^2x

=> INT = tanx + (tan^3x)/3 + C


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Answer 2

Answer:

Step-by-step explanation:

∫sec^4 x dx

∫sec^2 x sec^2 x dx

sec^2 x ∫sec^2dx - ∫2secxsecxtanxtanx dx

sec^2 xtanx - ∫2sec^2 x tan^2 x dx

sec^2 xtanx-2∫sec^2 x (sec^2 x-1) dx

sec^2 xtanx-2{∫sec^4 dx - ∫sec^2 x dx}

∫sec^4 x dx = sec^2 xtanx-2{∫sec^4 dx - ∫sec^2 x dx}

3∫sec^4 dx = sec^2 x tanx +2tanx

∫sec^4 x dx=sec^2 xtanx /3 +2tanx/3