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$\int\left(x^2+5\right)\ln\left(x\right)dx$

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Solution

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Final answer to the problem

$\left(\frac{x^{3}}{3}+5x\right)\ln\left|x\right|-5x+\frac{-x^{3}}{9}+C_0$
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We can solve the integral $\int\left(x^2+5\right)\ln\left(x\right)dx$ 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 limiti per sostituzione diretta 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 limiti per sostituzione diretta problems step by step online. int((x^2+5)ln(x))dx. We can solve the integral \int\left(x^2+5\right)\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

$\left(\frac{x^{3}}{3}+5x\right)\ln\left|x\right|-5x+\frac{-x^{3}}{9}+C_0$

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Function Plot

Plotting: $\left(\frac{x^{3}}{3}+5x\right)\ln\left(x\right)-5x+\frac{-x^{3}}{9}+C_0$

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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

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