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Find the integral $\int\frac{\left(u+1\right)^2}{u}du$

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Solution

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Final Answer

$\left(u+1\right)^2\ln\left(u\right)+2u-2u\ln\left(u\right)+\frac{1}{2}u^2-u^2\ln\left(u\right)+C_0$
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Step-by-step Solution

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Rewrite the fraction $\frac{\left(u+1\right)^2}{u}$ inside the integral as the product of two functions: $\left(u+1\right)^2\frac{1}{u}$

$\int\left(u+1\right)^2\frac{1}{u}du$

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$\int\left(u+1\right)^2\frac{1}{u}du$

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Learn how to solve integral calculus problems step by step online. Find the integral int(((u+1)^2)/u)du. Rewrite the fraction \frac{\left(u+1\right)^2}{u} inside the integral as the product of two functions: \left(u+1\right)^2\frac{1}{u}. We can solve the integral \int\left(u+1\right)^2\frac{1}{u}du by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v.

Final Answer

$\left(u+1\right)^2\ln\left(u\right)+2u-2u\ln\left(u\right)+\frac{1}{2}u^2-u^2\ln\left(u\right)+C_0$

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 integral of (((u+1)^2)/u)du using partial fractionsSolve integral of (((u+1)^2)/u)du using basic integralsSolve integral of (((u+1)^2)/u)du using u-substitutionSolve integral of (((u+1)^2)/u)du using trigonometric substitution

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Function Plot

Plotting: $\left(u+1\right)^2\ln\left(u\right)+2u-2u\ln\left(u\right)+\frac{1}{2}u^2-u^2\ln\left(u\right)+C_0$

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0
a
b
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n
u
v
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x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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