#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# what will be the integration of e^(x^2) ? solution should be with taking care of 12th standard student

2 years ago

2*X*e^(x^2)

The usual differentiation of e^x is e^x, this is the formula we'll use here.

As the term to be differentiated is e^(x^2)

On differentiating it would be e^(x^2) * (differentiation of x^2)

Differentiation of x^2 is 2x

Edit: I'm sry I didn't see that.

Integration of E^(x^2) would be (e^(x^2))/2x

The same logic applies here the only difference is we divide the term rather than multiplying it.

Formula is integral of e^xis E^x

Integral of e^(x^2) would be (e^(x^2)) divided by (differentiation of x^2)

2 years ago
Dear student
ere is no elementary function that describes the antiderivative of e^x^2. We can, however, express this integral in terms of an infinite series.
e^x=1+x+x^2/2!+x^3/3!+x^4/4!+⋯= ∑ n=0to ∞ x^n/n!
ex^2= ∑n=0 to ∞ x^2n/n!
∫∑ n=0 to ∞ x^2n/n!dx = ∑n=0 to ∞ x^(2n+1) /(2n+1)n!
Hence,
∫e^x^2 dx = ∑n=0 to ∞ x^(2n+1)/(2n+1)n!