Answer:
sec(4x) + C
Explanation:
original problem: ∫sec(4x)tan(x)dx
use integration by substitution (u-sub) by setting u = 4x
if u = 4x, then du/dx = 4 and du = 4dx (dx = du/4)
after substitution the integral is ∫sec(u)tan(u)(du/4)
move the 1/4 out of the integral by using the integral Constant rule to form 1/4∫sec(u)tan(u)du
the anti-derivative of sec(u)tan(u) is sec(u), memorize your trigonometric derivatives!!!!
after integration, we get sec(u)/4 + C , now plug u back into the equation
sec(4x) + C is the general solution
Answer:
Explanation:
The unification of Romania and Moldova (Romanian: Unirea Republicii Moldova cu România) is a popular concept in the two countries beginning with the late 1980s, during the collapse of communism. The Romanian Revolution in 1989 and the independence of Moldova in 1991
Important changes in the Middle East between the 13th and 15th centuries include the 13 Century end of the First Crusade and the capture/founding of Jerusalem. After that came the rise of the Mongol/Turkish/Ottoman Empire during the 14th Century. The Ottoman transcontinental Empire controlled much of North Africa, Western Asia, and Southeast Europe. This led to the creation of important transcontinental trade routes and a boom of economic trade between the continents.
Pushing the Mongols north and fighting them, and the rebuilding of Beijing caused the Chinese decision to abandon major expeditions.
