What is the integral of ((Inx)^2)/x ?

The integral of ((Inx)^2)/x is (I^2n^2x^2)/2+C

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integral of ((Inx)^2)/x

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the Power Rule

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

Multiply fractions:

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

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

Add a constant to the solution

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

What is the integral of ((Inx)^2)/x ?
The integral of ((Inx)^2)/x is (I^2n^2x^2)/2+C