zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的微积分 >

integral of 9cos(4x)cos(9x)

解答

\int 9 cos (4 x) cos (9 x) d x

解答

\frac{9}{2} (\frac{1}{5} sin (5 x) + \frac{1}{13} sin (13 x)) + C

求解步骤

\int 9 cos (4 x) cos (9 x) d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \int cos (4 x) cos (9 x) d x

使用三角恒等式改写

= 9 \cdot \int \frac{1}{2} (cos (13 x) + cos (- 5 x)) d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \frac{1}{2} \cdot \int cos (13 x) + cos (- 5 x) d x

化简

cos (13 x) + cos (- 5 x) : cos (5 x) + cos (13 x)

= 9 \cdot \frac{1}{2} \cdot \int cos (5 x) + cos (13 x) d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 9 \cdot \frac{1}{2} (\int cos (5 x) d x + \int cos (13 x) d x)

\int cos (5 x) d x = \frac{1}{5} sin (5 x)

\int cos (13 x) d x = \frac{1}{13} sin (13 x)

= 9 \cdot \frac{1}{2} (\frac{1}{5} sin (5 x) + \frac{1}{13} sin (13 x))

化简

9 \cdot \frac{1}{2} (\frac{1}{5} sin (5 x) + \frac{1}{13} sin (13 x)) : \frac{9}{2} (\frac{1}{5} sin (5 x) + \frac{1}{13} sin (13 x))

= \frac{9}{2} (\frac{1}{5} sin (5 x) + \frac{1}{13} sin (13 x))

解答补常数

= \frac{9}{2} (\frac{1}{5} sin (5 x) + \frac{1}{13} sin (13 x)) + C

作图

流行的例子

integral of-10csc^2(5x)cot^3(5x)

\int - 10 csc^{2} (5 x) cot^{3} (5 x) d x

integral of sqrt(x)sqrt(16-x)

\int x 16 - x d x

integral of (3sqrt(x))/(-2)

\int \frac{3 x}{- 2} d x

integral of (y^2)/((x^2+y^2)^{3/2)}

\int \frac{y ^{2}}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} d x

integral of 1/((1+sin(x))^2)

\int \frac{1}{( 1 + sin ( x ) ) ^{2}} d x