What is expand x^3(x^3+2x+3)^2dx ?

The solution to expand x^3(x^3+2x+3)^2dx is x^9dx+4x^7dx+6x^6dx+4x^5dx+12x^4dx+9x^3dx

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expand x^3(x^3+2x+3)^2dx

expand

x^{3} (x^{3} + 2 x + 3)^{2} d x

x^{9} d x + 4 x^{7} d x + 6 x^{6} d x + 4 x^{5} d x + 12 x^{4} d x + 9 x^{3} d x

Solution steps

x^{3} (x^{3} + 2 x + 3)^{2} d x

(x^{3} + 2 x + 3)^{2} = x^{6} + 4 x^{4} + 6 x^{3} + 4 x^{2} + 12 x + 9

= x^{3} (x^{6} + 4 x^{4} + 6 x^{3} + 4 x^{2} + 12 x + 9) d x

Distribute parentheses

= x^{3} d x x^{6} + x^{3} d x \cdot 4 x^{4} + x^{3} d x \cdot 6 x^{3} + x^{3} d x \cdot 4 x^{2} + x^{3} d x \cdot 12 x + x^{3} d x \cdot 9

= x^{6} x^{3} d x + 4 x^{4} x^{3} d x + 6 x^{3} x^{3} d x + 4 x^{3} x^{2} d x + 12 x^{3} x d x + 9 x^{3} d x

Simplify

x^{6} x^{3} d x + 4 x^{4} x^{3} d x + 6 x^{3} x^{3} d x + 4 x^{3} x^{2} d x + 12 x^{3} x d x + 9 x^{3} d x : x^{9} d x + 4 x^{7} d x + 6 x^{6} d x + 4 x^{5} d x + 12 x^{4} d x + 9 x^{3} d x

= x^{9} d x + 4 x^{7} d x + 6 x^{6} d x + 4 x^{5} d x + 12 x^{4} d x + 9 x^{3} d x

e^{2 x} (1 + e^{2 x})^{3} d x

(- 3) (4 x - 5 y = 3)

- 3 ((- 2, 1, 1) - (4, 3, 5))

\frac{( 4 + x ) ^{3}}{8}

3 (e^{3 t} + C e^{- t}) + 8 e^{- t}

What is expand x^3(x^3+2x+3)^2dx ?
The solution to expand x^3(x^3+2x+3)^2dx is x^9dx+4x^7dx+6x^6dx+4x^5dx+12x^4dx+9x^3dx