tích phân 5

Question

$ \int\limits_{}^{} \frac{dx}{cosx.cos(x +a )} $

$ \int\limits_{}^{} tan(x + \pi/3).cotg(x-\pi/6)dx $

score 5 · Answer 1

Ta có:
$\int\frac{dx}{\cos x\cos(x +a )}$
$=\int\frac{\cos x\sin(x+a)-\sin x\cos (x+a)}{\sin a\cos x\cos(x+a)}dx$
$=\frac{1}{\sin a}\int\left(\frac{d(\cos x)}{\cos x}-\frac{d(\cos(x+a))}{\cos(x+a)}\right)$
$=\frac{1}{\sin a}(\ln(\cos x)-\ln(\cos(x+a))+C$

score 5 · Answer 2

Bình chọn tăng 5 Bình chọn giảm

Ta có:
$\int\tan(x+\frac{\pi}{3})\cot(x-\frac{\pi}{6})dx$
$=-\int\tan^2(x+\frac{\pi}{3})dx$
$=-\int(1+\tan^2(x+\frac{\pi}{3}))d(x+\frac{\pi}{3})+\int dx$
$=x-\tan(x+\frac{\pi}{3})+C$