integral of (ln(10x))/x

解答

\int \frac{ln ( 10 x )}{x} d x

\frac{ln ^{2} ( 10 x )}{2} + C

求解步骤

\int \frac{ln ( 10 x )}{x} d x

使用换元积分法

= \int \frac{ln ( u )}{u} d u

使用换元积分法

= \int v d v

使用幂法则

= \frac{v ^{2}}{2}

代回

= \frac{ln ^{2} ( 10 x )}{2}

解答补常数

= \frac{ln ^{2} ( 10 x )}{2} + C

\int \frac{sin ( 5 x )}{cos ( 5 x )} d x

\frac{d y}{d x} = 8 x^{4} (6 + y^{2})^{\frac{3}{2}}

\int \frac{1}{1 - x ^{3}} d x

t an g e n t x^{2} - 5 x + 5

\int x^{3} x^{2} + 8 d x