Question

Integral de secante al cubo de 2x

Answer 1

Guíate con esto

$\int \sec^3y~dy = \int (1 + \tan^2y)\sec y~dy= \int \sec y~dy+\int\tan^2y\sec y~dy\\ \\ \int \sec^3y~dy =\ln |\sec y+\tan y|+\int \tan y~d(\sec y)\\ \\ \int \sec^3y~dy =\ln |\sec y+\tan y| +\sec y\tan y-\int\sec y~d(\tan y)\\ \\ \int \sec^3y~dy =\ln |\sec y+\tan y| +\sec y\tan y-\int\sec^3y~dy\\ \\ 2\int \sec^3y~dy =\ln |\sec y+\tan y| +\sec y\tan y\\ \\ \int \sec^3y~dy =\dfrac{1}{2}\ln |\sec y+\tan y| +\dfrac{1}{2}\sec y\tan y+C$