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(1+4x^4)(16x^3)

解答

\int 1 + 4 x^{4} (16 x^{3}) d x

解答

\frac{2}{3} (4 x^{4} + 1)^{\frac{3}{2}} + C

求解步骤

\int 1 + 4 x^{4} \cdot 16 x^{3} d x

提出常数:

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

= 16 \cdot \int 1 + 4 x^{4} x^{3} d x

使用换元积分法

= 16 \cdot \int \frac{1 + 4 u}{4} d u

提出常数:

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

= 16 \cdot \frac{1}{4} \cdot \int 1 + 4 u d u

使用换元积分法

= 16 \cdot \frac{1}{4} \cdot \int \frac{v}{4} d v

提出常数:

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

= 16 \cdot \frac{1}{4} \cdot \frac{1}{4} \cdot \int v d v

使用幂法则

= 16 \cdot \frac{1}{4} \cdot \frac{1}{4} \cdot \frac{2}{3} v^{\frac{3}{2}}

代回

= 16 \cdot \frac{1}{4} \cdot \frac{1}{4} \cdot \frac{2}{3} (1 + 4 x^{4})^{\frac{3}{2}}

化简

16 \cdot \frac{1}{4} \cdot \frac{1}{4} \cdot \frac{2}{3} (1 + 4 x^{4})^{\frac{3}{2}} : \frac{2}{3} (4 x^{4} + 1)^{\frac{3}{2}}

= \frac{2}{3} (4 x^{4} + 1)^{\frac{3}{2}}

解答补常数

= \frac{2}{3} (4 x^{4} + 1)^{\frac{3}{2}} + C

作图

流行的例子

integral of (x^2+2x-8)

\int (x^{2} + 2 x - 8) d x

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

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

integral of 5^{sin(x)}*cos(x)

\int 5^{s i n (x)} \cdot cos (x) d x

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

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

integral of 5xsqrt(8x+5)

\int 5 x 8 x + 5 d x