Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

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

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
÷
2

e
π
ln
log
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

$-\frac{1}{8}x^{4}\cos\left(x^2-9\right)+\left(\frac{9}{4}x^2-\frac{81}{8}\right)\cos\left(x^2-9\right)+\frac{16}{181}\sqrt{\frac{\sqrt{u+9}\sqrt{u}}{2}+9}\sqrt[4]{u+9}\sqrt[4]{u}\sin\left(\frac{\sqrt{\frac{\sqrt{u+9}\sqrt{u}}{2}+9}\sqrt{\frac{1}{2}\sqrt{u+9}\sqrt{u}}}{2}\right)+\frac{1}{4}\cos\left(u\right)+C_0$

Step-by-step explanation

Problem to solve:

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

Podemos resolver la integral $\int x^2\sin\left(2x\right)dx$ aplicando un cambio de variable. Sean $u$ y $du$

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

Despejando $dx$ de la ecuación anterior

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

Unlock this step-by-step solution!

Answer

$-\frac{1}{8}x^{4}\cos\left(x^2-9\right)+\left(\frac{9}{4}x^2-\frac{81}{8}\right)\cos\left(x^2-9\right)+\frac{16}{181}\sqrt{\frac{\sqrt{u+9}\sqrt{u}}{2}+9}\sqrt[4]{u+9}\sqrt[4]{u}\sin\left(\frac{\sqrt{\frac{\sqrt{u+9}\sqrt{u}}{2}+9}\sqrt{\frac{1}{2}\sqrt{u+9}\sqrt{u}}}{2}\right)+\frac{1}{4}\cos\left(u\right)+C_0$