Calculators AI Whiteboard Worksheets & Tests
Book solutions
Algebra Baldor
Go Premium Topics

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

Step-by-step Solution

Go!
Symbolic mode
Text mode
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
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
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

Final answer to the problem

$\frac{1}{1.5}t^{1.5}\ln\left|t\right|-\frac{1}{1.5}invfrac\left(1.5\right)t^{1.5}+C_0$
Got another answer? Verify it here!

Step-by-step Solution

How should I solve this problem?

  • Choose an option
  • 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
  • Load more...
Can't find a method? Tell us so we can add it.
1

We can solve the integral $\int t^{0.5}\ln\left(t\right)dt$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula

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

Learn how to solve problems step by step online.

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

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution

Learn how to solve problems step by step online. Solve the integral of logarithmic functions int(t^1/2ln(t))dt. We can solve the integral \int t^{0.5}\ln\left(t\right)dt by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v. Solve the integral to find v.

Final answer to the problem

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

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

Help us improve with your feedback!

Function Plot

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

SnapXam A2
Answer Assistant

beta
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
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:

Supercharge your math learning

By signing up, you agree to SnapXam's Terms and Privacy Policy.

Already have an account? Login here
Forgot your password?

Supercharge your math learning



Register here if you don't have an account.
Forgot your password?

Invest in your Education!

Help us make you learn faster

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Download complete solutions and keep them forever.

Premium access on our iOS and Android apps.

Join 500k+ students in problem solving.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account