Consider the integral, I=∫sec5dx Simplify the above, I=∫sec3xsec2xdx =sec3xtanx−∫3sec3xtan2xdx =sec3xtanx−3∫sec3x(1+sec2x)dx =sec3xtanx−3∫sec5xdx−3∫sec3xdx Further simplify the above, I=sec3xtanx−3I−3∫sec2x√1+tan2xdx Take tanx=t then 4I=sec3xtanx−3∫√t2+1dx 4I=sec3xtanx−