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Question

If sec4x dx=secmxtanxn+ktanx+C
(C is integration constant), then the value of m+2n+3k is equal to

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Solution

I=sec4x dx=secI2xsecII2x dx
Applying integration by parts
I=sec2xtanxtanx2secxsecxtanx dx =sec2xtanx2sec2x(sec2x1)dxI=sec2xtanx2I+2sec2x dx3I=sec2xtanx+2tanx+CI=sec2xtanx3+23tanx+Cm=2, n=3, k=23
m+2n+3k=2+6+2=10

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