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受欢迎的微积分 >

integral of (10800)/(9q^2+675)

解答

\int \frac{10800}{9 q ^{2} + 675} d q

解答

803 arctan (\frac{1}{5 3} q) + C

求解步骤

\int \frac{10800}{9 q ^{2} + 675} d q

提出常数:

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

= 10800 \cdot \int \frac{1}{9 q ^{2} + 675} d q

使用换元积分法

= 10800 \cdot \int \frac{1}{45 3 ( u ^{2} + 1 )} d u

提出常数:

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

= 10800 \cdot \frac{1}{45 3} \cdot \int \frac{1}{u ^{2} + 1} d u

使用积分常见定则:

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

= 10800 \cdot \frac{1}{45 3} arctan (u)

u = \frac{3}{15 3} q

代回

= 10800 \cdot \frac{1}{45 3} arctan (\frac{3}{15 3} q)

化简

10800 \cdot \frac{1}{45 3} arctan (\frac{3}{15 3} q) : 803 arctan (\frac{1}{5 3} q)

= 803 arctan (\frac{1}{5 3} q)

解答补常数

= 803 arctan (\frac{1}{5 3} q) + C

作图

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