What is expand x^3y*In(xy+1)dx ?

The solution to expand x^3y*In(xy+1)dx is nx^4y^2Idx+nx^3yIdx

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expand x^3y*In(xy+1)dx

expand

x^{3} y \cdot I n (x y + 1) d x

n x^{4} y^{2} I d x + n x^{3} y I d x

Solution steps

x^{3} y I n (x y + 1) d x

= n x^{3} y I (x y + 1) d x

Apply the distributive law:

a (b + c) = ab + a c

a = x^{3} y I n d x, b = x y, c = 1

= x^{3} y I n d xx y + x^{3} y I n d x \cdot 1

= n x^{3} x yy I d x + 1 \cdot n x^{3} y I d x

Simplify

n x^{3} x yy I d x + 1 \cdot n x^{3} y I d x : n x^{4} y^{2} I d x + n x^{3} y I d x

= n x^{4} y^{2} I d x + n x^{3} y I d x

(e^{2} + 2) (e^{2} - 2)

\frac{( x - 1 ) ^{2}}{x ^{2} - 2 x}

x^{3} y \cdot I n (x y + 1) d y

\frac{( x + 6 )}{2 ( x - 6 )}

x (x + 2)^{2} - x^{2} e + a^{4}

What is expand x^3y*In(xy+1)dx ?
The solution to expand x^3y*In(xy+1)dx is nx^4y^2Idx+nx^3yIdx