integral from 0 to 3 of (x/(1+x^4))

解答

\int_{0}^{3} (\frac{x}{1 + x ^{4}}) d x

\frac{1}{2} arctan (9)

十进制

0.73006 \dots

求解步骤

\int_{0}^{3} \frac{x}{1 + x ^{4}} d x

计算不定积分:

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

带入上下限计算后得:

\int_{0}^{3} (\frac{x}{1 + x ^{4}}) d x = \frac{1}{2} arctan (9) - 0

= \frac{1}{2} arctan (9) - 0

化简

= \frac{1}{2} arctan (9)

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