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 y/(sqrt(25-36y^4))

解答

\int \frac{y}{25 - 36 y ^{4}} d y

解答

\frac{1}{12} arcsin (\frac{6}{5} y^{2}) + C

求解步骤

\int \frac{y}{25 - 36 y ^{4}} d y

使用换元积分法

= \int \frac{1}{2 25 - 36 u ^{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 \frac{1}{25 - 36 u ^{2}} d u

使用三角换元法

= \frac{1}{2} \cdot \int \frac{1}{6} d v

提出常数:

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

= \frac{1}{2} \cdot \frac{1}{6} \cdot \int 1 d v

常数积分:

\int a d x = a x

= \frac{1}{2} \cdot \frac{1}{6} \cdot 1 \cdot v

代回

= \frac{1}{2} \cdot \frac{1}{6} \cdot 1 \cdot arcsin (\frac{6}{5} y^{2})

化简

\frac{1}{2} \cdot \frac{1}{6} \cdot 1 \cdot arcsin (\frac{6}{5} y^{2}) : \frac{1}{12} arcsin (\frac{6}{5} y^{2})

= \frac{1}{12} arcsin (\frac{6}{5} y^{2})

解答补常数

= \frac{1}{12} arcsin (\frac{6}{5} y^{2}) + C

作图

流行的例子

integral of (t^6)/(sqrt(1-t^{14))}

\int \frac{t ^{6}}{1 - t ^{14}} d t

limit as x approaches a+of g(x)

x \to a + lim (g (x))

integral of x^3*cos(x)

\int x^{3} \cdot cos (x) d x

derivative 9z^2e^z

d er i v a t i v e 9 z^{2} e^{z}

integral of x^5ln(8x)

\int x^{5} ln (8 x) d x