Question

Question #93667

Answer 1

`intxe^4dx=(e^4x^2)/2+"C"`

Explanation:

Given: `intxe^4dx` (unless you meant `intxe^(4x)dx`

In this example, `e^4` is a constant which we can pull out of the integral. Therefore we can rewrite the integral as:

`e^4*intxdx`

To find `intxdx` use the following princple:

`intx^adx=(x^(a+1))/(a+1)+"C";x>0`

So `intxdx=(x^(1+1))/(1+1)=x^2/2+"C"`

Multiplying `e^4` we get

`e^4*x^2/2+"C"=(e^4x^2)/2+"C"`