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Integrate the function $x\left(x+\frac{1}{\sqrt{x}}\right)$ from 0 to $1$

Step-by-step Solution

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acos
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sinh
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asinh
acosh
atanh
acoth
asech
acsch

Final Answer

$1$
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Step-by-step Solution

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1

Rewrite the integrand $x\left(x+\frac{1}{\sqrt{x}}\right)$ in expanded form

$\int_{0}^{1}\left(x^2+\frac{x}{\sqrt{x}}\right)dx$

Learn how to solve polynomial factorization problems step by step online.

$\int_{0}^{1}\left(x^2+\frac{x}{\sqrt{x}}\right)dx$

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Learn how to solve polynomial factorization problems step by step online. Integrate the function x(x+1/(x^1/2)) from 0 to 1. Rewrite the integrand x\left(x+\frac{1}{\sqrt{x}}\right) in expanded form. Expand the integral \int_{0}^{1}\left(x^2+\frac{x}{\sqrt{x}}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Simplify the fraction by x. The integral \int_{0}^{1} x^2dx results in: \frac{1}{3}.

Final Answer

$1$

Exact Numeric Answer

$1$

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Function Plot

Plotting: $x\left(x+\frac{1}{\sqrt{x}}\right)$

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1
2
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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
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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Main Topic: Polynomial Factorization

They are a group of techniques that help us rewrite polynomial expressions as a product of factors.

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