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 sqrt(2x+3)sin(sqrt(2x+3))

解答

\int 2 x + 3 sin (2 x + 3) d x

解答

- 2 x cos (2 x + 3) - cos (2 x + 3) + 2 sin (2 x + 3) 2 x + 3 + C

求解步骤

\int 2 x + 3 sin (2 x + 3) d x

使用换元积分法

= \int u sin (u) \frac{1}{2} d u

提出常数:

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

= \frac{1}{2} \cdot \int u sin (u) d u

使用换元积分法

= \frac{1}{2} \cdot \int 2 v^{2} sin (v) d v

提出常数:

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

= \frac{1}{2} \cdot 2 \cdot \int v^{2} sin (v) d v

使用分布积分法

= \frac{1}{2} \cdot 2 (- v^{2} cos (v) - \int - 2 v cos (v) d v)

\int - 2 v cos (v) d v = - 2 (v sin (v) + cos (v))

= \frac{1}{2} \cdot 2 (- v^{2} cos (v) - (- 2 (v sin (v) + cos (v))))

代回

= \frac{1}{2} \cdot 2 (- (2 x + 3)^{2} cos (2 x + 3) - (- 2 (2 x + 3 sin (2 x + 3) + cos (2 x + 3))))

化简

\frac{1}{2} \cdot 2 (- (2 x + 3)^{2} cos (2 x + 3) - (- 2 (2 x + 3 sin (2 x + 3) + cos (2 x + 3)))) : - 2 x cos (2 x + 3) - cos (2 x + 3) + 2 sin (2 x + 3) 2 x + 3

= - 2 x cos (2 x + 3) - cos (2 x + 3) + 2 sin (2 x + 3) 2 x + 3

解答补常数

= - 2 x cos (2 x + 3) - cos (2 x + 3) + 2 sin (2 x + 3) 2 x + 3 + C

作图

流行的例子

integral of 6xsqrt(x+5)

\int 6 x x + 5 d x

integral of xsqrt(x^2-2x+2)

\int x x^{2} - 2 x + 2 d x

integral of 1/(x(1+5ln(x)))

\int \frac{1}{x ( 1 + 5 ln ( x ) )} d x

integral of 1/(u^2-2)

\int \frac{1}{u ^{2} - 2} d u

integral of ((9+8x))/(1+x^2)

\int \frac{( 9 + 8 x )}{1 + x ^{2}} d x