$\int e^{3x^2}dx$

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?

  • Choisir une option
  • Weierstrass Substitution
  • Produit de binômes avec terme commun
  • Load more...
Can't find a method? Tell us so we can add it.
1

Apply the formula: $e^x$$=\sum_{n=0}^{\infty } \frac{x^n}{n!}$, where $2.718281828459045=e$, $x=3x^2$ and $2.718281828459045^x=e^{3x^2}$

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

Learn how to solve intégrales des fonctions exponentielles 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 intégrales des fonctions exponentielles problems step by step online. int(e^(3x^2))dx. Apply the formula: e^x=\sum_{n=0}^{\infty } \frac{x^n}{n!}, where 2.718281828459045=e, x=3x^2 and 2.718281828459045^x=e^{3x^2}. Apply the formula: \int\sum_{a}^{b} \frac{x}{c}dx=\sum_{a}^{b} \frac{1}{c}\int xdx, where a=n=0, b=\infty , c=n! and x=\left(3x^2\right)^n. Apply the formula: \left(ab\right)^n=a^nb^n, where a=3 and b=x^2. Apply the formula: \int cxdx=c\int xdx, where c=3^n and x=x^{2n}.

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:

Your Personal Math Tutor. Powered by AI

Available 24/7, 365.

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

Includes multiple solving methods.

Download complete solutions and keep them forever.

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