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# Find the integral $\int4x\sin\left(x^3\right)dx$

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##  Final answer to the problem

$4\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(6n+5\right)}}{\left(6n+5\right)\left(2n+1\right)!}+C_0$
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##  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
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1

The integral of a function times a constant ($4$) is equal to the constant times the integral of the function

$4\int x\sin\left(x^3\right)dx$

Learn how to solve integral calculus problems step by step online.

$4\int x\sin\left(x^3\right)dx$

Learn how to solve integral calculus problems step by step online. Find the integral int(sin(x^3)4x)dx. The integral of a function times a constant (4) is equal to the constant times the integral of the function. Rewrite the function \sin\left(x^3\right) as it's representation in Maclaurin series expansion. Simplify \left(x^3\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 3 and n equals 2n+1. Solve the product 3\left(2n+1\right).

##  Final answer to the problem

$4\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(6n+5\right)}}{\left(6n+5\right)\left(2n+1\right)!}+C_0$

##  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

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7
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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: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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