Integration Of Sec 3 X. Web question 2 (5 points) use integration by parts with u = sec x, d v = sec 2 x d x to solve the integral ∫ sec 3 x d x. Integration of the form f(p)p'(x)
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Web integral of sec^3x blackpenredpen 1.03m subscribers subscribe 8.1k share save 626k views 7 years ago integral of sec^3x with integration by parts integral of sin^3 (x) by trig. U = sec x, v = sec 2 x. U = secx and dv = sec2xdx ⇒ du = secxtanxdx and v = tanx, = secxtanx −∫secxtan2xdx by tan2x = sec2x − 1 = secxtanx −∫(sec3x −secx)dx since ∫sec3xdx = i, =. Web what is the integral of s e c 3 x? Feel free to comment any questions you may have. Another method would be to note that tan x sec 3 x = ( tan x sec x) ( sec 2 x) and that the differential of sec x is tan x sec x. Dec 22, 2014 i = ∫sec3xdx by integration by pats with: Web this is a standard integral. Thus, we have ∫( secx(secx +tanx) secx +tanx)dx ∫ sec2x + secxtanx secx + tanx dx now, make the following substitution: ∴ i = ∫ 1 cos3x ⋅ cosx sinx dx = ∫ 1 cos2xsinx dx.
Integration of the form f(p)p'(x) A method called spotting the presence of the derivative. [2] he applied his result to a problem concerning nautical tables. Web ∫ sec 3 x d x = ∫ sec x ( sec 2 x d x) let tan x = t sec 2 x d x = d t and sec x = 1 + t 2 which changes our integral to ∫ 1 + t 2 d t which is a standard integral which evaluates to t 1 + t 2 2 + log ( t + 1 + t 2) 2. Feel free to comment any questions you may have. Thus, we have ∫( secx(secx +tanx) secx +tanx)dx ∫ sec2x + secxtanx secx + tanx dx now, make the following substitution: Web hence ∫ sec 3 x d x = 2 1. Now back substitute t = tan x in answer share cite follow edited may 26, 2018 at 21:30 michael hardy 1 Web integral of sec^3x blackpenredpen 1.03m subscribers subscribe 8.1k share save 626k views 7 years ago integral of sec^3x with integration by parts integral of sin^3 (x) by trig. U = secx +tanx du = (secxtanx +sec2x)dx = (sec2x + secxtanx)dx ∫ sec 3 x d x = ∫ sec x sec 2 x d x from integration by parts: