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Integrate $\int x\sqrt{4x^2-5}dx$

Step-by-step Solution

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Final Answer

$\frac{2}{3}\sqrt{\left(x^2-\frac{5}{4}\right)^{3}}+C_0$
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Step-by-step Solution

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First, factor the terms inside the radical by $4$ for an easier handling

$\int x\sqrt{4\left(x^2-\frac{5}{4}\right)}dx$

Learn how to solve integrals with radicals problems step by step online.

$\int x\sqrt{4\left(x^2-\frac{5}{4}\right)}dx$

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Learn how to solve integrals with radicals problems step by step online. Integrate int(x(4x^2-5)^1/2)dx. First, factor the terms inside the radical by 4 for an easier handling. Taking the constant out of the radical. We can solve the integral \int2x\sqrt{x^2-\frac{5}{4}}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.

Final Answer

$\frac{2}{3}\sqrt{\left(x^2-\frac{5}{4}\right)^{3}}+C_0$

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Function Plot

Plotting: $\frac{2}{3}\sqrt{\left(x^2-\frac{5}{4}\right)^{3}}+C_0$

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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

How to improve your answer:

Main Topic: Integrals with Radicals

Integrals with radicals are those integrals that contain a radical (square root, cubic, etc.) in the numerator or denominator of the integral.

Used Formulas

2. See formulas

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