integral of ((Inx)^2)/x

解答

\int \frac{( I n x ) ^{2}}{x} d x

\frac{I ^{2} n ^{2} x ^{2}}{2} + C

求解步骤

\int \frac{( I n x ) ^{2}}{x} d x

化简

\frac{( I n x ) ^{2}}{x} : I^{2} n^{2} x

= \int I^{2} n^{2} x d x

提出常数:

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

= I^{2} n^{2} \cdot \int x d x

使用幂法则

= I^{2} n^{2} \frac{x ^{2}}{2}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{I ^{2} n ^{2} x ^{2}}{2}

解答补常数

= \frac{I ^{2} n ^{2} x ^{2}}{2} + C

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