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受欢迎的微积分 >

积分 (log_{10}((1+x)^2))/(x^2)

解答

积分

\frac{lo g _{10} ( ( 1 + x ) ^{2} )}{x ^{2}}

解答

- \frac{2 lo g _{10} ( 1 + x )}{x} + \frac{2}{ln ( 10 )} (ln ∣ x ∣ - ln ∣ x + 1 ∣) + C

求解步骤

\int \frac{lo g _{10} ( ( 1 + x ) ^{2} )}{x ^{2}} d x

使用分布积分法

= - \frac{lo g _{10} ( ( 1 + x ) ^{2} )}{x} - \int - \frac{2}{ln ( 10 ) x ( x + 1 )} d x

\int - \frac{2}{ln ( 10 ) x ( x + 1 )} d x = - \frac{2}{ln ( 10 )} (ln ∣ x ∣ - ln ∣ x + 1 ∣)

= - \frac{lo g _{10} ( ( 1 + x ) ^{2} )}{x} - (- \frac{2}{ln ( 10 )} (ln ∣ x ∣ - ln ∣ x + 1 ∣))

化简

- \frac{lo g _{10} ( ( 1 + x ) ^{2} )}{x} - (- \frac{2}{ln ( 10 )} (ln ∣ x ∣ - ln ∣ x + 1 ∣)) : - \frac{2 lo g _{10} ( 1 + x )}{x} + \frac{2}{ln ( 10 )} (ln ∣ x ∣ - ln ∣ x + 1 ∣)

= - \frac{2 lo g _{10} ( 1 + x )}{x} + \frac{2}{ln ( 10 )} (ln ∣ x ∣ - ln ∣ x + 1 ∣)

解答补常数

= - \frac{2 lo g _{10} ( 1 + x )}{x} + \frac{2}{ln ( 10 )} (ln ∣ x ∣ - ln ∣ x + 1 ∣) + C

作图

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