What is expand Zex(2+3ex)5dx ?

The solution to expand Zex(2+3ex)5dx is 10eZxdx+15e^2Zx^2dx

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expand Zex(2+3ex)5dx

expand

Z e x (2 + 3 e x) 5 d x

10 e Z x d x + 15 e^{2} Z x^{2} d x

Solution steps

Z e x (2 + 3 e x) \cdot 5 d x

= 5 e Z x (2 + 3 e x) d x

Apply the distributive law:

a (b + c) = ab + a c

a = Z e x \cdot 5 d x, b = 2, c = 3 e x

= Z e x \cdot 5 d x \cdot 2 + Z e x \cdot 5 d x \cdot 3 e x

= 5 \cdot 2 e Z x d x + 5 \cdot 3 ee Z xx d x

Simplify

5 \cdot 2 e Z x d x + 5 \cdot 3 ee Z xx d x : 10 e Z x d x + 15 e^{2} Z x^{2} d x

= 10 e Z x d x + 15 e^{2} Z x^{2} d x

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sin (t) u (t - π)

What is expand Zex(2+3ex)5dx ?
The solution to expand Zex(2+3ex)5dx is 10eZxdx+15e^2Zx^2dx