# What is #int x*e^(x^2) dx# ?

So:

By signing up, you agree to our Terms of Service and Privacy Policy

To integrate ( x \cdot e^{x^2} ) with respect to ( x ), you can use substitution. Let ( u = x^2 ), then ( du = 2x , dx ). Rewriting the integral:

[ \int x \cdot e^{x^2} , dx = \frac{1}{2} \int e^u , du ]

Now, integrate ( e^u ) with respect to ( u ):

[ \int e^u , du = e^u + C ]

Substitute back ( u = x^2 ):

[ \frac{1}{2} \int e^{x^2} , dx = \frac{1}{2} e^{x^2} + C ]

So, ( \int x \cdot e^{x^2} , dx = \frac{1}{2} e^{x^2} + 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.

- Calc 2 questions super lost! Evaluate a power series to find the sum of the series, or show that the series diverges. (If a series diverges, enter DIVERGES.)? (a) #11/1-11/3+11/5-11/7+11/9-11/11+....# (b)#sum_(n=2)^oo ((-1)^n(8^n))/(n!) #
- How do I write #(5/(1*2))+(5/(2*3))+(5/(3*4))+...+(5/n(n+1))+...#in summation notation, and how can I tell if the series converges?
- How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given #ln(1/2)+ln(2/3)+ln(3/4)+...+ln(n/(n+1))+...#?
- How do you use the limit comparison test for #sum (2x^4)/(x^5+10)# n=1 to #n=oo#?
- Solve the following (limit; L'Hospital's Rule)?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7