Evaluate the following indefinite integrals using Solution c

Solution

?(cos ^-3 2?* sin 2?) d? Lets simplify it a little we know that sinx/cosx = tanx so we can rewrite our equation as ?sin(2?)/cos^3(2?) d? i.e. ?sin(2?)/ cos^2(2?)*cos(2?) d? ?sec^2(2?)tan(2?)d? Take the substitution as u = 2? du = 2d? du/2 = d? We will get the integral as ?sec^2(u)tan(u)du/2 1/2?sec^2(u)tan(u)du Now, take again substitution as s = tanu ds = sec^2u du Applying the substitution method in our integral, we will get 1/2?sds applying the power rule of integral will give 1/2[s^2/2] + c Now, use the reverse substitution method. we will get 1/4[tan^2(2?)] + c Hope this will help you!