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Solve the integral of logarithmic functions $\int t^{0.5}\ln\left(t\right)dt$

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Solving: $\int t^{0.5}\ln\left(t\right)dt$
Solve instead: $\int\left(sqrt\left(t\right)ln\left(t\right)\right)dx$

Solution

Formulas

Videos

Worked example: problem involving definite integral (algebraic) | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=vYix-RPhT64

Using one to one property to solve logarithmic equation

https://www.youtube.com/watch?v=9aCtoIRZWBU

Finding the domain vertical asymptote and x intercepts of a logarithm

https://www.youtube.com/watch?v=k36n5uACiac

How to find the solutions when solving a logarithmic equation

https://www.youtube.com/watch?v=JrivLbx0o50

Analyzing problems involving definite integrals | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=U4dtruMdQ7Y

Calculus - Take the derivative of the equation of a circle with respect to t, d(x^2 + y^2 = d^2)dt

https://www.youtube.com/watch?v=acDi9r48KTA

Function Plot

Plotting: $\frac{1}{1.5}t^{1.5}\ln\left(t\right)-\frac{1}{1.5}invfrac\left(1.5\right)t^{1.5}+C_0$

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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
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:

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Main Topic: Integrals involving Logarithmic Functions

They are those integrals where the function that we are integrating is composed only of combinations of logarithmic functions.

Used Formulas

See formulas (2)

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