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Show full steps. sec 3x dxSolution Integrate.pdf

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Show full steps. sec 3x dx Solution Integrate by parts: u = sec(x) dv = sec²(x) dx du = sec(x)*tan(x) dx v = tan(x) K = sec(x)*tan(x) - ?sec(x)*tan²(x) dx Recall the identity 1 + tan²(x) = sec²(x). K = sec(x)*tan(x) - ?sec³(x) dx + ?sec(x) dx K = sec(x)*tan(x) - K + ln|sec(x) + tan(x)| + C K = ?sec³(x) dx = [sec(x)*tan(x) + ln|sec(x) + tan(x)|]/2 + C.

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Show full steps. sec 3x dx Solution Integrate by parts: u = sec(x) dv = sec²(x) dx du = sec(x)*tan(x) dx v = tan(x) K = sec(x)*tan(x) - ?sec(x)*tan²(x) dx Recall the identity 1 + tan²(x) = sec²(x). K = sec(x)*tan(x) - ?sec³(x) dx + ?sec(x) dx K = sec(x)*tan(x) - K + ln|sec(x) + tan(x)| + C K = ?sec³(x) dx = [sec(x)*tan(x) + ln|sec(x) + tan(x)|]/2 + C

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Show full steps. sec 3x dxSolution Integrate.pdf

  • 1. Show full steps. sec 3x dx Solution Integrate by parts: u = sec(x) dv = sec²(x) dx du = sec(x)*tan(x) dx v = tan(x) K = sec(x)*tan(x) - ?sec(x)*tan²(x) dx Recall the identity 1 + tan²(x) = sec²(x). K = sec(x)*tan(x) - ?sec³(x) dx + ?sec(x) dx K = sec(x)*tan(x) - K + ln|sec(x) + tan(x)| + C K = ?sec³(x) dx = [sec(x)*tan(x) + ln|sec(x) + tan(x)|]/2 + C