What is expand parts[(-30x^2-3x)e^{-5x}]dx ?

The solution to expand parts[(-30x^2-3x)e^{-5x}]dx is -30ae^{-5x}prtsx^2dx-3ae^{-5x}prtsxdx

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expand parts[(-30x^2-3x)e^{-5x}]dx

expand

p a r t s [(- 30 x^{2} - 3 x) e^{- 5 x}] d x

- 30 a e^{- 5 x} p r t s x^{2} d x - 3 a e^{- 5 x} p r t s x d x

Solution steps

p a r t s ((- 30 x^{2} - 3 x) e^{- 5 x}) d x

Remove parentheses:

(a) = a

= p a r t s (- 30 x^{2} - 3 x) e^{- 5 x} d x

= a e^{- 5 x} p r t s (- 30 x^{2} - 3 x) d x

Apply the distributive law:

a (b - c) = ab - a c

a = p a r t s e^{- 5 x} d x, b = - 30 x^{2}, c = 3 x

= p a r t s e^{- 5 x} d x (- 30 x^{2}) - p a r t s e^{- 5 x} d x \cdot 3 x

Apply minus-plus rules

+ (- a) = - a

= - 30 a e^{- 5 x} p r t s x^{2} d x - 3 a e^{- 5 x} p r t s x d x

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What is expand parts[(-30x^2-3x)e^{-5x}]dx ?
The solution to expand parts[(-30x^2-3x)e^{-5x}]dx is -30ae^{-5x}prtsx^2dx-3ae^{-5x}prtsxdx