Integrate the function $\frac{4x^3-10x+20}{2x+3}$

Step-by-step Solution

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Final answer to the problem

$\frac{2}{3}x^{3}-\frac{3}{2}x^2-\frac{1}{2}x+\frac{43}{4}\ln\left|2x+3\right|+C_0$
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Step-by-step Solution

How should I solve this problem?

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

Find the integral

$\int\frac{4x^3-10x+20}{2x+3}dx$

Learn how to solve integral calculus problems step by step online.

$\int\frac{4x^3-10x+20}{2x+3}dx$

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Unlock the first 3 steps of this solution

Learn how to solve integral calculus problems step by step online. Integrate the function (4x^3-10x+20)/(2x+3). Find the integral. Divide 4x^3-10x+20 by 2x+3. Resulting polynomial. Expand the integral \int\left(2x^{2}-3x-\frac{1}{2}+\frac{43}{2\left(2x+3\right)}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately.

Final answer to the problem

$\frac{2}{3}x^{3}-\frac{3}{2}x^2-\frac{1}{2}x+\frac{43}{4}\ln\left|2x+3\right|+C_0$

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Function Plot

Plotting: $\frac{2}{3}x^{3}-\frac{3}{2}x^2-\frac{1}{2}x+\frac{43}{4}\ln\left(2x+3\right)+C_0$

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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: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Used Formulas

See formulas (5)

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