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

Step-by-step Solution

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e
π
ln
log
log
lim
d/dx
Dx
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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

Final answer to the problem

$t^{0.5}x\ln\left|t\right|+C_0$
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Step-by-step Solution

How should I solve this problem?

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  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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1

The integral of a constant is equal to the constant times the integral's variable

$t^{0.5}x\ln\left|t\right|$
2

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$t^{0.5}x\ln\left|t\right|+C_0$

Final answer to the problem

$t^{0.5}x\ln\left|t\right|+C_0$

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Function Plot

Plotting: $t^{0.5}x\ln\left(t\right)+C_0$

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Got a different answer? Verify it!

Go!
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
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

How to improve your answer:

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 (1)

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