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# Find the integral $\int\left(x^{\frac{3}{2}}+2x+1\right)dx$

## Step-by-step Solution

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###  Videos

$\frac{2}{5}\sqrt{x^{5}}+x^2+x+C_0$
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##  Step-by-step Solution 

Problem to solve:

$\int\left(x^{\frac{3}{2}}+2x+1\right)dx$

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1

Simplifying

$\int\left(\sqrt{x^{3}}+2x+1\right)dx$

Learn how to solve integral calculus problems step by step online.

$\int\left(\sqrt{x^{3}}+2x+1\right)dx$

Learn how to solve integral calculus problems step by step online. Find the integral int(x^(3/2)+2x+1)dx. Simplifying. Expand the integral \int\left(\sqrt{x^{3}}+2x+1\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\sqrt{x^{3}}dx results in: \frac{2}{5}\sqrt{x^{5}}. The integral \int2xdx results in: x^2.

$\frac{2}{5}\sqrt{x^{5}}+x^2+x+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int(x^(3/2)+2x+1)dx using partial fractionsSolve int(x^(3/2)+2x+1)dx using basic integralsSolve int(x^(3/2)+2x+1)dx using u-substitutionSolve int(x^(3/2)+2x+1)dx using integration by partsSolve int(x^(3/2)+2x+1)dx using trigonometric substitution

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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

### Main topic:

Integral Calculus

~ 0.06 s

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