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Solve the integral of logarithmic functions $\int\left(\pi +1\right)\frac{\ln\left(x+1\right)^2}{x+1}dx$

Step-by-step Solution

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Final answer to the problem

$\frac{-8.2831853-8.2831853\ln\left(x+1\right)}{-x-1}+\frac{4.1415927\ln\left(x+1\right)^2x}{x+1}+\frac{8.2831853}{x+1}+\frac{-8.2831853\ln\left(x+1\right)}{-x-1}+\frac{-4.1415927\ln\left(x+1\right)^2}{-x-1}+1.3805309\ln\left(x+1\right)^{3}-4.1415927\ln\left(x+1\right)^2+C_0$
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Step-by-step Solution

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We can solve the integral $\int\left(\pi +1\right)\frac{\ln\left(x+1\right)^2}{x+1}dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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Learn how to solve problems step by step online. Solve the integral of logarithmic functions int((ln(x+1)^2)/(x+1)(pi+1))dx. We can solve the integral \int\left(\pi +1\right)\frac{\ln\left(x+1\right)^2}{x+1}dx 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. Solve the integral.

Final answer to the problem

$\frac{-8.2831853-8.2831853\ln\left(x+1\right)}{-x-1}+\frac{4.1415927\ln\left(x+1\right)^2x}{x+1}+\frac{8.2831853}{x+1}+\frac{-8.2831853\ln\left(x+1\right)}{-x-1}+\frac{-4.1415927\ln\left(x+1\right)^2}{-x-1}+1.3805309\ln\left(x+1\right)^{3}-4.1415927\ln\left(x+1\right)^2+C_0$

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 (ln(x+1)^2)/(x+1)(\pi +1)dx using basic integralsSolve integral of (ln(x+1)^2)/(x+1)(\pi +1)dx using u-substitutionSolve integral of (ln(x+1)^2)/(x+1)(\pi +1)dx using tabular integration

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Function Plot

Plotting: $\frac{-8.2831853-8.2831853\ln\left(x+1\right)}{-x-1}+\frac{4.1415927\ln\left(x+1\right)^2x}{x+1}+\frac{8.2831853}{x+1}+\frac{-8.2831853\ln\left(x+1\right)}{-x-1}+\frac{-4.1415927\ln\left(x+1\right)^2}{-x-1}+1.3805309\ln\left(x+1\right)^{3}-4.1415927\ln\left(x+1\right)^2+C_0$

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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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