# Step-by-step Solution

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## Step-by-step Solution

Problem to solve:

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

Solving method

Learn how to solve calculus problems step by step online.

$\begin{matrix}P(x)=x^2 \\ T(x)=\cos\left(2x\right)\end{matrix}$

Learn how to solve calculus problems step by step online. Find the integral int(x^2cos(2x))dx. We can solve the integral \int x^2\cos\left(2x\right)dx by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form \int P(x)T(x) dx. P(x) is typically a polynomial function and T(x) is a transcendent function such as \sin(x), \cos(x) and e^x. The first step is to choose functions P(x) and T(x). Derive P(x) until it becomes 0. Integrate T(x) as many times as we have had to derive P(x), so we must integrate \cos\left(2x\right) a total of 3 times. With the derivatives and integrals of both functions we build the following table.

## Final Answer

$\frac{1}{2}x^2\sin\left(2x\right)+\frac{1}{2}x\cos\left(2x\right)-\frac{1}{4}\sin\left(2x\right)+C_0$
SnapXam A2
Answer Assistant

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m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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

### Tips on how to improve your answer:

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

Calculus

10. See formulas

~ 0.5 s