Find the integral $\int e^{3x^2}dx$

Step-by-step Solution

Go!
Symbolic mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Final answer to the problem

$\sum_{n=0}^{\infty } \frac{3^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$
Got another answer? Verify it here!

Step-by-step Solution

How should I solve this problem?

  • Choose an option
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • Load more...
Can't find a method? Tell us so we can add it.
1

Rewrite the function $e^{3x^2}$ as it's representation in Maclaurin series expansion

Learn how to solve discriminant of quadratic equation problems step by step online.

$\int\sum_{n=0}^{\infty } \frac{\left(3x^2\right)^n}{n!}dx$

With a free account, access a part of this solution

Unlock the first 3 steps of this solution

Learn how to solve discriminant of quadratic equation problems step by step online. Find the integral int(e^(3x^2))dx. Rewrite the function e^{3x^2} as it's representation in Maclaurin series expansion. We can rewrite the power series as the following. The power of a product is equal to the product of it's factors raised to the same power. The integral of a function times a constant (3^n) is equal to the constant times the integral of the function.

Final answer to the problem

$\sum_{n=0}^{\infty } \frac{3^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Help us improve with your feedback!

Function Plot

Plotting: $\sum_{n=0}^{\infty } \frac{3^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Discriminant of Quadratic Equation

Quadratic equations are those algebraic equations of the form ax^2+bx+c, where a, b, and c are constant values. The discriminant of a quadratic equation is calculated using the formula D=b^2-4ac, and it helps us to determine how many roots an equation of this type has. When D>0 the equation has two real roots, when D<0 the equation has no real roots, and when D=0 the equation has a repeated real root.

Your Personal Math Tutor. Powered by AI

Available 24/7, 365 days a year.

Complete step-by-step math solutions. No ads.

Choose between multiple solving methods.

Download solutions in PDF format and keep them forever.

Unlimited practice with our AI whiteboard.

Premium access on our iOS and Android apps.

Join 500k+ students in problem solving.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.

Create an Account