ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Solve the trigonometric integral $\int\sin\left(x^2\right)dx$

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

$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(4n+3\right)}}{\left(4n+3\right)\left(2n+1\right)!}+C_0$
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
Can't find a method? Tell us so we can add it.
1

Rewrite the function $\sin\left(x^2\right)$ as it's representation in Maclaurin series expansion

$\int\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{\left(2n+1\right)!}\left(x^2\right)^{\left(2n+1\right)}dx$

Learn how to solve trigonometric integrals problems step by step online.

$\int\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{\left(2n+1\right)!}\left(x^2\right)^{\left(2n+1\right)}dx$

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sin(x^2))dx. Rewrite the function \sin\left(x^2\right) as it's representation in Maclaurin series expansion. Simplify \left(x^2\right)^{\left(2n+1\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2n+1. Solve the product 2\left(2n+1\right). We can rewrite the power series as the following.

##  Final answer to the problem

$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(4n+3\right)}}{\left(4n+3\right)\left(2n+1\right)!}+C_0$

##  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

SnapXam A2

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

###  Main Topic: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.