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# Integrate the function $\left(x+1\right)^2+\left(x+1\right)^2$ from 0 to $1$

## Step-by-step Solution

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$\frac{14}{3}$
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##  Step-by-step Solution 

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Combining like terms $\left(x+1\right)^2$ and $\left(x+1\right)^2$

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

Learn how to solve definite integrals problems step by step online.

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

Learn how to solve definite integrals problems step by step online. Integrate the function (x+1)^2+(x+1)^2 from 0 to 1. Combining like terms \left(x+1\right)^2 and \left(x+1\right)^2. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. Apply the formula: \int\left(x+a\right)^ndx=\frac{\left(x+a\right)^{\left(n+1\right)}}{n+1}+C, where a=1 and n=2. Simplify the expression inside the integral.

$\frac{14}{3}$

$4.6667$

##  Explore different ways to solve this problem

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a
b
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
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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: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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