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Find the integral $\int\frac{x}{x^2+1}dx$

Step-by-step Solution

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e
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ln
log
log
lim
d/dx
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θ
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<
>=
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sin
cos
tan
cot
sec
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asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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$\ln\left(\sqrt{x^2+1}\right)+C_0$
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Step-by-step Solution

Problem to solve:

$\int\frac{x}{x^2+1}dx$

Choose the solving method

1

We can solve the integral $\int\frac{x}{x^2+1}dx$ by applying integration method of trigonometric substitution using the substitution

$x=\tan\left(\theta \right)$

Learn how to solve integrals of rational functions problems step by step online.

$x=\tan\left(\theta \right)$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int(x/(x^2+1))dx. We can solve the integral \int\frac{x}{x^2+1}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get. Applying the trigonometric identity: \tan(x)^2+1=\sec(x)^2.

$\ln\left(\sqrt{x^2+1}\right)+C_0$
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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

$\int\frac{x}{x^2+1}dx$