Find the integral $\int2x\cos\left(x^3\right)dx$

Step-by-step Solution

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Final answer to the problem

$2\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(6n+2\right)}}{\left(6n+2\right)\left(2n\right)!}+C_0$
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Step-by-step Solution

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  • Integrate by partial fractions
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  • Product of Binomials with Common Term
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The integral of a function times a constant ($2$) is equal to the constant times the integral of the function

Learn how to solve integrals of polynomial functions problems step by step online.

$2\int x\cos\left(x^3\right)dx$

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Learn how to solve integrals of polynomial functions problems step by step online. Find the integral int(2xcos(x^3))dx. The integral of a function times a constant (2) is equal to the constant times the integral of the function. Rewrite the function \cos\left(x^3\right) as it's representation in Maclaurin series expansion. Simplify \left(x^3\right)^{2n} 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. Bring the outside term x inside the power serie.

Final answer to the problem

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

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Function Plot

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

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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

How to improve your answer:

Main Topic: Integrals of Polynomial Functions

Integrals of polynomial functions.

Used Formulas

See formulas (2)

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