# Step-by-step Solution

Go!
1
2
3
4
5
6
7
8
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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## Step-by-step explanation

Problem to solve:

$\int\left(xln\left(x^3\right)\right)dx$

Learn how to solve trigonometric integrals problems step by step online.

$\int3x\ln\left(x\right)dx$

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(x*ln(x^3))dx. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The integral of a constant by a function is equal to the constant multiplied by the integral of the function. Use the integration by parts theorem to calculate the integral \int x\ln\left(x\right)dx, using the following formula. First, identify u and calculate du.

$\frac{1}{4}\left(-\frac{3}{2}x^2+3x^2\ln\left(x\right)\right)+C_0$

### Problem Analysis

$\int\left(xln\left(x^3\right)\right)dx$

### Main topic:

Trigonometric integrals

~ 0.35 seconds