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Integrate $\int\frac{\sin\left(\sqrt{x}\right)}{\sqrt{x}}dx$

Used Formulas

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Derivatives of trigonometric functions

· Derivative of the sine function
$\frac{d}{dx}\left(\sin\left(\theta \right)\right)=\frac{d}{dx}\left(\theta \right)\cos\left(\theta \right)$

Basic Derivatives

· Power rule for derivatives
$\frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

Basic Integrals

· Constant factor Rule
$\int cxdx=c\int xdx$

Integration Techniques

· Integration by Parts
$\int udv=uv - \int vdu$
· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$

Trigonometric Integrals

· Integral of the cosine function
$\int\cos\left(\theta \right)dx=\sin\left(\theta \right)+C$
· Integral of the sine function
$\int\sin\left(\theta \right)dx=-\cos\left(\theta \right)+C$

Function Plot

Plotting: $-2\cos\left(\sqrt{x}\right)+C_0$

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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

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