nguyên hàm 12

Question

1,   $\int\limits\cos ^43xdx$

2,   $\int\limits\frac{dx}{\sin ^22x}$

3,   $\int\limits\frac{dx}{\sin ^2(1-3x)}$

score 0 · Answer 1

$I_2 =\int \dfrac{1}{\sin^2 2x}dx =\dfrac{1}{2}\int \dfrac{d(2x)}{\sin^2 2x} =-\dfrac{1}{2}\cot 2x + C$

$I_3 = \int \dfrac{1}{\sin^2 (1-3x)}dx =-\dfrac{1}{3}\int \dfrac{d(1-3x)}{\sin^2 (1-3x)}=\dfrac{1}{3}\cot (1-3x) +C$

score 0 · Answer 2

$I_1 =\int \cos^4 3x dx =\dfrac{1}{4} \int (1+\cos 6x)^2 dx =\dfrac{1}{4}\int (1 +2\cos 6x + \cos^2 6x)dx$

$=\dfrac{1}{4}x + \dfrac{1}{12}\sin 6x +\dfrac{1}{4}\int \cos^2 6x dx =\dfrac{1}{4}x + \dfrac{1}{12}\sin 6x+\dfrac{1}{8}\int (1+\cos 12x)dx$

$=\dfrac{3}{8}x + \dfrac{1}{12}\sin 6x+\dfrac{1}{96}\sin 12x + C$

2 Đáp án