How do you integrate #int x^n*e^(x^n)dx# using integration by parts?
We are aware of that
By signing up, you agree to our Terms of Service and Privacy Policy
To integrate ( \int x^n e^{x^n} , dx ) using integration by parts, let ( u = x^n ) and ( dv = e^{x^n} , dx ). Then, ( du = n x^{n-1} , dx ) and ( v = \int e^{x^n} , dx ).
This integral for ( v ) doesn't have a simple closed form, but we can represent it using the Exponential Integral function, denoted as ( \text{Ei}(x) ). So, ( v = \text{Ei}(x^n) ).
Now, we apply the integration by parts formula:
[ \int u , dv = uv - \int v , du ]
Substitute the values:
[ \int x^n e^{x^n} , dx = x^n \text{Ei}(x^n) - \int \text{Ei}(x^n) \cdot n x^{n-1} , dx ]
This integral may not simplify further depending on the context.
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.
- How do you integrate #int e^x sin sqrtx dx # using integration by parts?
- How do you use partial fraction decomposition to decompose the fraction to integrate #1/(1+e^x) #?
- How do you integrate #(ln x) ^ 2 / x ^ 2#?
- How do you integrate #x*arctan(x) dx#?
- How come integration of sin²2x cos 2x dx become [sin^3 (2x) ]/6?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7