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Integrate the function $\frac{2x^3+18}{\left(x+3\right)\left(x^2+9\right)}$ from 0 to $3$

Step-by-step Solution

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Solution

Final Answer

$1.656615$
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Step-by-step Solution

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$\int_{0}^{3}\frac{2x^3+18}{x^{3}+9x+3x^2+27}dx$

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$\int_{0}^{3}\frac{2x^3+18}{x^{3}+9x+3x^2+27}dx$

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Learn how to solve problems step by step online. Integrate the function (2x^3+18)/((x+3)(x^2+9)) from 0 to 3. Expand. Divide 2x^3+18 by x^{3}+9x+3x^2+27. Resulting polynomial. Simplify the expression inside the integral.

Final Answer

$1.656615$

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

Solve integral of ((2x^3+18)/(x+3)(x^2+9))dx from 0 to 3 using partial fractionsSolve integral of ((2x^3+18)/(x+3)(x^2+9))dx from 0 to 3 using basic integralsSolve integral of ((2x^3+18)/(x+3)(x^2+9))dx from 0 to 3 using u-substitutionSolve integral of ((2x^3+18)/(x+3)(x^2+9))dx from 0 to 3 using integration by partsSolve integral of ((2x^3+18)/(x+3)(x^2+9))dx from 0 to 3 using trigonometric substitution

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Function Plot

Plotting: $\frac{2x^3+18}{\left(x+3\right)\left(x^2+9\right)}$

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1
2
3
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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

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