Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

Trigonometric integral int(sin(2*x)*x^2)dx

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Answer

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

Step-by-step explanation

Problem to solve:

$\int\sin\left(2x\right)x^2dx$
1

Solve the integral $\int x^2\sin\left(2x\right)dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=2x \\ du=2dx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{2}=dx$

Unlock this step-by-step solution!

Answer

$-\frac{1}{2}x^2\cos\left(2x\right)+\frac{1}{4}\left(2x\sin\left(2x\right)+1-2\sin\left(x\right)^2\right)+C_0$
$\int\sin\left(2x\right)x^2dx$

Main topic:

Trigonometric integrals

Used formulas:

6. See formulas

Time to solve it:

~ 1.86 seconds

Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!