What is expand (ax^2y^4e^{x^3y^4}+3/(x^2+1))dx ?

The solution to expand (ax^2y^4e^{x^3y^4}+3/(x^2+1))dx is ae^{x^3y^4}x^2y^4dx+(3dx)/(x^2+1)

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expand (ax^2y^4e^{x^3y^4}+3/(x^2+1))dx

expand

(a x^{2} y^{4} e^{x^{3} y^{4}} + \frac{3}{x ^{2} + 1}) d x

a e^{x^{3} y^{4}} x^{2} y^{4} d x + \frac{3 d x}{x ^{2} + 1}

Solution steps

(a x^{2} y^{4} e^{x^{3} y^{4}} + \frac{3}{x ^{2} + 1}) d x

= (a e^{x^{3} y^{4}} x^{2} y^{4} + \frac{3}{x ^{2} + 1}) d x

Apply the distributive law:

a (b + c) = ab + a c

a = d x, b = a x^{2} y^{4} e^{x^{3} y^{4}}, c = \frac{3}{x ^{2} + 1}

= d x a x^{2} y^{4} e^{x^{3} y^{4}} + d x \frac{3}{x ^{2} + 1}

= a e^{x^{3} y^{4}} x^{2} y^{4} d x + \frac{3}{x ^{2} + 1} d x

Multiply

\frac{3}{x ^{2} + 1} d x : \frac{3 d x}{x ^{2} + 1}

= a e^{x^{3} y^{4}} x^{2} y^{4} d x + \frac{3 d x}{x ^{2} + 1}

(4 - e^{x}) e^{x}

\frac{( 2 x ^{2} + x ) ^{2}}{4}

\frac{s}{( s + 2 ) ^{2} ( s ^{2} + 25 )}

- \frac{( r + θ ) ( r - θ )}{θ ^{2}}

\frac{( 3 x + 2 ) ( 9 x - 2 )}{3}

What is expand (ax^2y^4e^{x^3y^4}+3/(x^2+1))dx ?
The solution to expand (ax^2y^4e^{x^3y^4}+3/(x^2+1))dx is ae^{x^3y^4}x^2y^4dx+(3dx)/(x^2+1)