Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

Solve the trigonometric integral $\int x\cos\left(3x\right)dx$

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

$\frac{1}{3}x\sin\left(3x\right)+\frac{1}{9}\cos\left(3x\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(x\cos3x\right)dx$
1

Solve the integral $\int x\cos\left(3x\right)dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=3x \\ du=3dx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{3}=dx$

Unlock this step-by-step solution!

Answer

$\frac{1}{3}x\sin\left(3x\right)+\frac{1}{9}\cos\left(3x\right)+C_0$
$\int\left(x\cos3x\right)dx$

Main topic:

Trigonometric integrals

Related formulas:

3. See formulas

Time to solve it:

~ 0.1 seconds