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 2x(1+x^2)^{23}

解答

\int 2 x (1 + x^{2})^{23} d x

解答

\frac{1}{24} (1 + x^{2})^{24} + C

求解步骤

\int 2 x (1 + x^{2})^{23} d x

提出常数:

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

= 2 \cdot \int x (1 + x^{2})^{23} d x

使用换元积分法

= 2 \cdot \int \frac{u ^{23}}{2} d u

提出常数:

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

= 2 \cdot \frac{1}{2} \cdot \int u^{23} d u

使用幂法则

= 2 \cdot \frac{1}{2} \cdot \frac{u ^{24}}{24}

u = 1 + x^{2}

代回

= 2 \cdot \frac{1}{2} \cdot \frac{( 1 + x ^{2} ) ^{24}}{24}

化简

2 \cdot \frac{1}{2} \cdot \frac{( 1 + x ^{2} ) ^{24}}{24} : \frac{1}{24} (1 + x^{2})^{24}

= \frac{1}{24} (1 + x^{2})^{24}

解答补常数

= \frac{1}{24} (1 + x^{2})^{24} + C

作图

流行的例子

integral of-csc^2(5/2)x

\int - csc^{2} (\frac{5}{2}) x d x

integral of 2x^2cos(2pi)x^3

\int 2 x^{2} cos (2 π) x^{3} d x

integral of (y^3-y^2+1)/((y^2+2y+2)^2)

\int \frac{y ^{3} - y ^{2} + 1}{( y ^{2} + 2 y + 2 ) ^{2}} d y

integral of (4x+7)^9

\int (4 x + 7)^{9} d x

integral of 1/((x-1)^2(x+4)^2)

\int \frac{1}{( x - 1 ) ^{2} ( x + 4 ) ^{2}} d x