What is the integral of (inx)^2 ?

The integral of (inx)^2 is i^2n^2x^3-(2i^2n^2x^3)/3+C

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integral of (inx)^2

\int (in x)^{2} d x

i^{2} n^{2} x^{3} - \frac{2 i ^{2} n ^{2} x ^{3}}{3} + C

Solution steps

\int (in x)^{2} d x

Apply Integration By Parts

: i^{2} n^{2} x^{3} - \int 2 i^{2} n^{2} x^{2} d x

= i^{2} n^{2} x^{3} - \int 2 i^{2} n^{2} x^{2} d x

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

= i^{2} n^{2} x^{3} - \frac{2 i ^{2} n ^{2} x ^{3}}{3}

Add a constant to the solution

= i^{2} n^{2} x^{3} - \frac{2 i ^{2} n ^{2} x ^{3}}{3} + C

x \to \infty lim (1 + x)

y = 2 (x + 1), y = 3 (x + 1), x = 5

\frac{d}{d x} (x^{2} + y^{3})

y \frac{d y}{d x} = x - 1

\frac{1}{5 - 5 x ^{3}}

What is the integral of (inx)^2 ?
The integral of (inx)^2 is i^2n^2x^3-(2i^2n^2x^3)/3+C