integral of ln|x|sin(x)

解答

\int ln ∣ x ∣ sin (x) d x

- ln ∣ x ∣ cos (x) + Ci (x) + C

求解步骤

\int ln ∣ x ∣ sin (x) d x

使用分布积分法

= - ln ∣ x ∣ cos (x) - \int - \frac{cos ( x )}{x} d x

\int - \frac{cos ( x )}{x} d x = - Ci (x)

= - ln ∣ x ∣ cos (x) - (- Ci (x))

化简

= - ln ∣ x ∣ cos (x) + Ci (x)

解答补常数

= - ln ∣ x ∣ cos (x) + Ci (x) + C

d er i v a t i v e 9 x^{3} (x^{2} - 2)

\int \frac{3 - 18 x}{4 - 9 x ^{2}} d x

\int \frac{1}{( 1 - 6 x ) ^{4}} d x

in v erse l a pl a ce \frac{( s + 1 )}{( s ^{2} + s + 1 )}

x \to + 4 lim (5)