How do you integrate #x^2 e^-5x dx#?
Hello,
Utilize the formula for integration by parts:
You could make things simpler:
Lastly, enter that into the expression above:
By signing up, you agree to our Terms of Service and Privacy Policy
To integrate ( x^2 e^{-5x} , dx ), you can use integration by parts. Let ( u = x^2 ) and ( dv = e^{-5x} , dx ). Then, ( du = 2x , dx ) and ( v = -\frac{1}{5} e^{-5x} ).
Now, applying the integration by parts formula:
[ \int u , dv = uv - \int v , du ]
We have:
[ \int x^2 e^{-5x} , dx = -\frac{x^2}{5} e^{-5x} - \int -\frac{2x}{5} e^{-5x} , dx ]
Integrating the second term again by parts:
Let ( u = x ) and ( dv = e^{-5x} , dx ). Then, ( du = dx ) and ( v = -\frac{1}{5} e^{-5x} ).
[ -\frac{x^2}{5} e^{-5x} - \left( -\frac{x}{5} e^{-5x} - \int -\frac{1}{5} e^{-5x} , dx \right) ]
[ -\frac{x^2}{5} e^{-5x} + \frac{x}{5} e^{-5x} - \frac{1}{25} e^{-5x} + C ]
So, the integral of ( x^2 e^{-5x} , dx ) is ( -\frac{x^2}{5} e^{-5x} + \frac{x}{5} e^{-5x} - \frac{1}{25} e^{-5x} + C ), where ( C ) is the constant of integration.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- What is #F(x) = int e^(x-2) - x dx# if #F(0) = 1 #?
- How do you find the integral of #(x^2 - 1)^(1/2)#?
- How do you integrate #int x^3 sqrt(-x^2 - 8x-41)dx# using trigonometric substitution?
- How do you integrate #int e^x cos x dx # using integration by parts?
- How do you evaluate the integral #int (sin^2x-cos^2x)/cosx# from #[-pi/4, pi/4]#?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7