Nguyên hàm 12

T

trantien.hocmai

$\int \frac{sin2x+cos2x}{sinx+cosx}dx= \int \frac{1+sin2x-2sin^2x}{sinx+cosx}dx$
$ \int \frac{(sinx+cosx)^2-2sin^2x}{sinx+cosx}dx=\int(sinx+cosx)dx-\int \frac{2sin^2x}{sinx+cosx}dx$
$=\int(sinx+cosx)dx-\int \frac{1}{sinx+cosx}dx+\int \frac{cos2x}{sinx+cosx}dx$
$=\sqrt{2}\int sin(x+\frac{\pi}{4})dx-\frac{1}{\sqrt{2}}\int \frac{1}{sin(x+\frac{\pi}{4})}dx+\int(cosx-sinx)dx$
tới đây tự làm tiếp nhá
 
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