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Solve the integral of logarithmic functions $\int x\ln\left(x+1\right)dx$

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 Solution

 Videos

Solving exponential equation | Exponential and logarithmic functions | Algebra II | Khan Academy

https://www.youtube.com/watch?v=7Ig6kVZaWoU

Calculus - Using power rule with square root to take derivative on a logarithm, d(ln(sqrt(x+1)))/dx

https://www.youtube.com/watch?v=vbgVpjL8ucU

Algebra 2 - Converting an equation to exponential form and then solving log3 (4x-17) = 5

https://www.youtube.com/watch?v=JJCuM8NcWH8

Condense a natural logarithmic expression

https://www.youtube.com/watch?v=OBWqxPUL3YI

Algebra 2 - Solving for a variable by converting to exponential form log4 (4x-20) = 5

https://www.youtube.com/watch?v=HNPmnB-KG88

Algebra 2 - Solve an equation to factor by converting to exponential form logx (5x) = 2

https://www.youtube.com/watch?v=vD-gS0AaAdU

 Function Plot

Plotting: $\frac{1}{2}x^2\ln\left(x+1\right)-\frac{1}{2}\ln\left(2x+2\right)+\frac{1}{2}x-\frac{1}{4}x^2+C_0$

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1

2

3

4

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

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

 How to improve your answer:

 Main Topic: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.

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