$\int\ln\left(x^2+2\right)dx$

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Final answer to the problem

$\left(x^2+2\right)\ln\left|x^2+2\right|-x^2+C_1$
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Step-by-step Solution

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Apply the formula: $\int\ln\left(x+b\right)dx$$=\left(x+b\right)\ln\left(x+b\right)-\left(x+b\right)+C$, where $b=2$, $x=x^2$ and $x+b=x^2+2$

$\left(x^2+2\right)\ln\left|x^2+2\right|-\left(x^2+2\right)$

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$\left(x^2+2\right)\ln\left|x^2+2\right|-\left(x^2+2\right)$

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Learn how to solve problems step by step online. int(ln(x^2+2))dx. Apply the formula: \int\ln\left(x+b\right)dx=\left(x+b\right)\ln\left(x+b\right)-\left(x+b\right)+C, where b=2, x=x^2 and x+b=x^2+2. Apply the formula: -\left(a+b\right)=-a-b, where a=x^2, b=2, -1.0=-1 and a+b=x^2+2. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C. We can combine and rename -2 and C_0 as other constant of integration.

Final answer to the problem

$\left(x^2+2\right)\ln\left|x^2+2\right|-x^2+C_1$

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Function Plot

Plotting: $\left(x^2+2\right)\ln\left(x^2+2\right)-x^2+C_1$

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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

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