What is the integral of 1/(x(Inx)^2) ?

The integral of 1/(x(Inx)^2) is -1/(2I^2n^2x^2)+C

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integral of 1/(x(Inx)^2)

\int \frac{1}{x ( I n x ) ^{2}} d x

- \frac{1}{2 I ^{2} n ^{2} x ^{2}} + C

Solution steps

\int \frac{1}{x ( I n x ) ^{2}} d x

Simplify

(I n x)^{2} x : I^{2} n^{2} x^{3}

= \int \frac{1}{I ^{2} n ^{2} x ^{3}} d x

Take the constant out:

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

= \frac{1}{I ^{2} n ^{2}} \cdot \int \frac{1}{x ^{3}} d x

Apply the Power Rule

: - \frac{1}{2 x ^{2}}

= \frac{1}{I ^{2} n ^{2}} (- \frac{1}{2 x ^{2}})

Simplify

\frac{1}{I ^{2} n ^{2}} (- \frac{1}{2 x ^{2}}) : - \frac{1}{2 I ^{2} n ^{2} x ^{2}}

= - \frac{1}{2 I ^{2} n ^{2} x ^{2}}

Add a constant to the solution

= - \frac{1}{2 I ^{2} n ^{2} x ^{2}} + C

\frac{d}{d x} (tan (x) d x)

\int e^{\frac{2 x}{5}} d x

\frac{1}{1 - x}, 20

\int 6 x y d x

\frac{d y}{d x}, (4 x + 4 y) 3 = 64 x^{3} + 64 y^{3}

What is the integral of 1/(x(Inx)^2) ?
The integral of 1/(x(Inx)^2) is -1/(2I^2n^2x^2)+C