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Integrate the function $x^2\ln\left(x\right)$ from $1$ to $6$

Step-by-step Solution

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Solution

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Final answer to the problem

$\frac{6^{3}\ln\left|6\right|}{3}- \frac{1^{3}\ln\left|1\right|}{3}-\frac{215}{9}$
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Step-by-step Solution

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

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

Learn how to solve differential equations problems step by step online.

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

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Learn how to solve differential equations problems step by step online. Integrate the function x^2ln(x) from 1 to 6. We can solve the integral \int x^2\ln\left(x\right)dx 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

$\frac{6^{3}\ln\left|6\right|}{3}- \frac{1^{3}\ln\left|1\right|}{3}-\frac{215}{9}$

Exact Numeric Answer

$105.117793$

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Function Plot

Plotting: $x^2\ln\left(x\right)$

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a
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m
n
u
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w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
◻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: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

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