How do you integrate ∫dx(9x2−25)32 using trig substitutions? Calculus Techniques of Integration Integration by Trigonometric Substitution 1 Answer Narad T. · mason m Nov 24, 2016 The answer is =−x25⋅√9x2−25+C Explanation: We use sec2u=1+tan2u Let's use the substitution x=5secu3 ⇒, dx=5secutanudu3 ∫dx(9x2−25)32=∫5secutanudu3(9⋅259sec2u−25)32 =∫5secutanudu3⋅125(tan3u) =175∫secudutan2u =175∫cos2uducosusin2u =175∫cosudusin2u Let v=sinu,⇒dv=cosudu Therefore, 175∫cosudusin2u=175∫dvv2 =175∫v−2dv=175v−1−1=−175v =−175sinu x=5secu3 ⇒, cosu=53x sin2u=1−cos2u=1−259x2=9x2−259x2 1sinu=3x√9x2−25 Therefore, ∫dx(9x2−25)32=(−175)⋅3x√9x2−25+C =−x25⋅√9x2−25+C Answer link Related questions How do you find the integral ∫1x2⋅√x2−9dx ? How do you find the integral ∫x3√x2+9dx ? How do you find the integral ∫x3⋅√9−x2dx ? How do you find the integral ∫x3√16−x2dx ? How do you find the integral ∫√x2−1xdx ? How do you find the integral ∫√x2−9x3dx ? How do you find the integral ∫x√x2+x+1dx ? How do you find the integral ∫dt√t2−6t+13 ? How do you find the integral ∫x⋅√1−x4dx ? How do you prove the integral formula ∫dx√x2+a2=ln(x+√x2+a2)+C ? See all questions in Integration by Trigonometric Substitution Impact of this question 3738 views around the world You can reuse this answer Creative Commons License