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受欢迎的微积分 >

integral of 1/(xsqrt(4x^4-1))

解答

\int \frac{1}{x 4 x ^{4} - 1} d x

解答

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

求解步骤

\int \frac{1}{x 4 x ^{4} - 1} d x

使用换元积分法

= \int \frac{1}{4 u 4 u - 1} d u

提出常数:

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

= \frac{1}{4} \cdot \int \frac{1}{u 4 u - 1} d u

使用换元积分法

= \frac{1}{4} \cdot \int \frac{2}{v ^{2} + 1} d v

提出常数:

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

= \frac{1}{4} \cdot 2 \cdot \int \frac{1}{v ^{2} + 1} d v

使用积分常见定则:

\int \frac{1}{v ^{2} + 1} d v = arctan (v)

= \frac{1}{4} \cdot 2 arctan (v)

代回

= \frac{1}{4} \cdot 2 arctan (4 x^{4} - 1)

化简

\frac{1}{4} \cdot 2 arctan (4 x^{4} - 1) : \frac{1}{2} arctan (4 x^{4} - 1)

= \frac{1}{2} arctan (4 x^{4} - 1)

解答补常数

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

作图

流行的例子

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\int_{- 2}^{1} (- x^{2} - x + 2) d x

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\int 3 25 - x d x

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\int_{- 2}^{0} (7 x^{2} + 7 x) d x

integral of 2sin(t)

\int 2 sin (t) d t

limit as h approaches 0 of ((x+h)^{2/3}-(x^{2/3}))/h

h \to 0 lim \frac{( x + h ) ^{\frac{2}{3}} - ( x ^{\frac{2}{3}} )}{h}