What is the integral of (int)^2 ?

The integral of (int)^2 is i^2n^2t^3-(2i^2n^2t^3)/3+C

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integral of (int)^2

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

y = - 18

\frac{d}{d x} (2 sec^{2} (x^{7}))

\frac{1}{2 x}, at x = 4

x \to 8 + lim (x - 8)

\frac{d x}{d t} = x^{2} - 2 x + 2

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