展开 (7(2+3sin(2x))(2x+3sin^2(x))^{4/3})/3

解答

展开

\frac{7 ( 2 + 3 sin ( 2 x ) ) ( 2 x + 3 sin ^{2} ( x ) ) ^{\frac{4}{3}}}{3}

\frac{14 ( 2 x + 3 sin ^{2} ( x ) ) ^{\frac{4}{3}}}{3} + 7 sin (2 x) (2 x + 3 sin^{2} (x))^{\frac{4}{3}}

求解步骤

\frac{7 ( 2 + 3 sin ( 2 x ) ) ( 2 x + 3 sin ^{2} ( x ) ) ^{\frac{4}{3}}}{3}

乘开

7 (2 + 3 sin (2 x)) (2 x + 3 sin^{2} (x))^{\frac{4}{3}} : 14 (2 x + 3 sin^{2} (x))^{\frac{4}{3}} + 21 sin (2 x) (2 x + 3 sin^{2} (x))^{\frac{4}{3}}

= \frac{14 ( 2 x + 3 sin ^{2} ( x ) ) ^{\frac{4}{3}} + 21 sin ( 2 x ) ( 2 x + 3 sin ^{2} ( x ) ) ^{\frac{4}{3}}}{3}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{14 ( 2 x + 3 sin ^{2} ( x ) ) ^{\frac{4}{3}} + 21 sin ( 2 x ) ( 2 x + 3 sin ^{2} ( x ) ) ^{\frac{4}{3}}}{3} = \frac{14 ( 2 x + 3 sin ^{2} ( x ) ) ^{\frac{4}{3}}}{3} + \frac{21 sin ( 2 x ) ( 2 x + 3 sin ^{2} ( x ) ) ^{\frac{4}{3}}}{3}

= \frac{14 ( 2 x + 3 sin ^{2} ( x ) ) ^{\frac{4}{3}}}{3} + \frac{21 sin ( 2 x ) ( 2 x + 3 sin ^{2} ( x ) ) ^{\frac{4}{3}}}{3}

数字相除:

\frac{21}{3} = 7

= \frac{14 ( 2 x + 3 sin ^{2} ( x ) ) ^{\frac{4}{3}}}{3} + 7 sin (2 x) (2 x + 3 sin^{2} (x))^{\frac{4}{3}}

e x p an d \frac{4 x ^{2}}{( 2 + x ) ( 3 + x )}

e x p an d \frac{25 ( x ^{2} - 1 )}{( x ^{2} + 1 ) ^{2}}

e x p an d x^{4} - 2 x - 16 x^{2} + 2 x + 15

e x p an d \frac{( 4 a + 1 ) ^{2}}{16}

e x p an d e^{8 (3 - t)}