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受欢迎的微积分 >

integral of 7/(xsqrt(49-(ln(x))^2))

解答

\int \frac{7}{x 49 - ( ln ( x ) ) ^{2}} d x

解答

7 arcsin (\frac{1}{7} ln (x)) + C

求解步骤

\int \frac{7}{x 49 - ( ln ( x ) ) ^{2}} d x

提出常数:

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

= 7 \cdot \int \frac{1}{x 49 - ( ln ( x ) ) ^{2}} d x

化简

= 7 \cdot \int \frac{1}{x 49 - ln ^{2} ( x )} d x

使用换元积分法

= 7 \cdot \int \frac{1}{49 - u ^{2}} d u

使用三角换元法

= 7 \cdot \int 1 d v

常数积分:

\int a d x = a x

= 7 \cdot 1 \cdot v

代回

= 7 \cdot 1 \cdot arcsin (\frac{1}{7} ln (x))

化简

= 7 arcsin (\frac{1}{7} ln (x))

解答补常数

= 7 arcsin (\frac{1}{7} ln (x)) + C

作图

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