Tính nguyên hàm

Question

Tính nguyên hàm $ y=\int\limits_{}^{}\frac{\tan( x+\frac{\pi }{4})}{\cos 2x} $

score 0 · Answer 1

$\int\limits\frac{tan(x+\frac{\pi }{4})}{cos2x}dx=\int\limits\frac{tan(x+\frac{\pi }{4})}{sin(2x+\frac{\pi }{2})}dx$

$=\int\limits\frac{tan(x+\frac{\pi }{4})}{2sin(x+\frac{\pi }{4})cos(x+\frac{\pi }{4})}dx$

$=\frac{1}{2}\int\limits\frac{1}{cos^2(x+\frac{\pi }{4})}dx$

$=\frac{1}{2}tan(x+\frac{\pi }{4})+C$.

1 Đáp án