Buscar

Loading [MathJax]/jax/output/HTML-CSS/jax.js

7.2E: Ejercicios para la Sección 7.2
https://espanol.libretexts.org/Matematicas/Libro%3A_Calculo_(OpenStax)/07%3A_T%C3%A9cnicas_de_Integraci%C3%B3n/7.02%3A_Integrales_trigonom%C3%A9tricas/7.2E%3A_Ejercicios_para_la_Secci%C3%B3n_7.2
$\displaystyle ∫\tan^2x\sec x\,dx \quad = \quad \tfrac{1}{2}\sec x\tan x−\tfrac{1}{2}\ln(\sec x+\tan x)+C$ \(\displaystyle ∫\sec^4x\,dx \quad = \quad \frac{2\tan x}{3}+\tfrac{1}{3}\sec^2 x\tan x=\ta... $\displaystyle ∫\tan^2x\sec x\,dx \quad = \quad \tfrac{1}{2}\sec x\tan x−\tfrac{1}{2}\ln(\sec x+\tan x)+C$ $\displaystyle ∫\sec^4x\,dx \quad = \quad \frac{2\tan x}{3}+\tfrac{1}{3}\sec^2 x\tan x=\tan x+\frac{\tan^3x}{3}+C$ $\displaystyle y = \int \sqrt{\tan x}\sec^4x \, dx \quad = \quad \tfrac{2}{3}\left(\tan x\right)^{3/2} + \tfrac{2}{7}\left(\tan x\right)^{7/2}+C= \tfrac{2}{21}\left(\tan x\right)^{3/2}\left[ 7 + 3\tan^2 x \right]+C$

Search