What is the integral of ln^2(x^{16}) ?

The integral of ln^2(x^{16}) is 256xln^2(x)-32(16xln(x)-16x)+C

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integral of ln^2(x^{16})

\int ln^{2} (x^{16}) d x

256 x ln^{2} (x) - 32 (16 x ln (x) - 16 x) + C

Solution steps

\int ln^{2} (x^{16}) d x

Apply Integration By Parts

: x ln^{2} (x^{16}) - \int 32 ln (x^{16}) d x

= x ln^{2} (x^{16}) - \int 32 ln (x^{16}) d x

\int 32 ln (x^{16}) d x = 32 (16 x ln (x) - 16 x)

= x ln^{2} (x^{16}) - 32 (16 x ln (x) - 16 x)

Simplify

x ln^{2} (x^{16}) - 32 (16 x ln (x) - 16 x) : 256 x ln^{2} (x) - 32 (16 x ln (x) - 16 x)

= 256 x ln^{2} (x) - 32 (16 x ln (x) - 16 x)

Add a constant to the solution

= 256 x ln^{2} (x) - 32 (16 x ln (x) - 16 x) + C

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What is the integral of ln^2(x^{16}) ?
The integral of ln^2(x^{16}) is 256xln^2(x)-32(16xln(x)-16x)+C