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Find the integral $\int\frac{x^2}{\sqrt{x^2+6}}dx$

Used formulas

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Solution

Formulas

Videos

Basic Integrals

· Constant factor Rule
$\int cxdx=c\int xdx$
· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$

Derivatives of trigonometric functions

$\frac{d}{dx}\left(\sec\left(x\right)\right)=\frac{d}{dx}\left(x\right)\sec\left(x\right)\tan\left(x\right)$

Basic Derivatives

· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

Trigonometric Integrals

$\int\sec\left(x\right)^2dx=\tan\left(x\right)+C$
$\int\sec\left(x\right)\tan\left(x\right)^2dx=\int\sec\left(x\right)^3dx-\int\sec\left(x\right)dx$
$\int\sec\left(x\right)dx=\ln\left(\sec\left(x\right)+\tan\left(x\right)\right)+C$
$\int\sec\left(x\right)^ndx=\frac{\sin\left(x\right)\sec\left(x\right)^{\left(n-1\right)}}{n-1}+\frac{n-2}{n-1}\int\sec\left(x\right)^{\left(n-2\right)}dx$

Integration Techniques

· Integration by Parts
$\int udv=uv - \int vdu$
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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
D□x
∫
∫◻
|◻|
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

How to improve your answer:

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Main topic:

Integrals of Rational Functions

Used formulas:

9. See formulas

Related topics:

Integrals of Rational FunctionsIntegral CalculusCalculusIndefinite IntegralsIntegralFactorizationIntegration by Trigonometric SubstitutionIntegration Techniques

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