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

Step-by-step Solution

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atanh
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Final Answer

$-\cos\left(x\right)+\ln\left(x\right)+C_0$
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Step-by-step Solution

Problem to solve:

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

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.

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

Unlock the first 2 steps of this solution!

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. 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).

Final Answer

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

Go!
1
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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

Useful tips on how to improve your answer:

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

Main topic:

Integral Calculus

Used formulas:

2. See formulas

Time to solve it:

~ 0.05 s

Related topics:

Integral CalculusCalculus