Try now NerdPal! Our new app on iOS and Android

# Find the integral $\int\frac{x\sin\left(x\right)+1}{x}dx$

## Step-by-step Solution

Go!
Math mode
Text mode
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
|◻|
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

###  Videos

$-\cos\left(x\right)+\ln\left(x\right)+C_0$
Got another answer? Verify it here!

##  Step-by-step Solution 

Problem to solve:

$\int\frac{x\sin\left(x\right)+1}{x}dx$

Specify the solving method

1

Expand the fraction $\frac{x\sin\left(x\right)+1}{x}$ into $2$ simpler fractions with common denominator $x$

$\int\left(\frac{x\sin\left(x\right)}{x}+\frac{1}{x}\right)dx$

Learn how to solve integral calculus problems step by step online.

$\int\left(\frac{x\sin\left(x\right)}{x}+\frac{1}{x}\right)dx$

Learn how to solve integral calculus problems step by step online. Find the integral int((xsin(x)+1)/x)dx. Expand the fraction \frac{x\sin\left(x\right)+1}{x} into 2 simpler fractions with common denominator x. Simplify the resulting fractions. Expand the integral \int\left(\sin\left(x\right)+\frac{1}{x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\sin\left(x\right)dx results in: -\cos\left(x\right).

$-\cos\left(x\right)+\ln\left(x\right)+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int((xsin(x)+1)/x)dx using basic integralsSolve int((xsin(x)+1)/x)dx using u-substitutionSolve int((xsin(x)+1)/x)dx using integration by partsSolve int((xsin(x)+1)/x)dx using tabular integration

SnapXam A2

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
|◻|
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

### Main topic:

Integral Calculus

~ 0.04 s

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account