Integrate the function $\frac{x^4+3x^2+4}{x+1}$

Step-by-step Solution

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Final answer to the problem

$\frac{x^{4}}{4}+\frac{-x^{3}}{3}+2x^2-4x+8\ln\left|x+1\right|+C_0$
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Step-by-step Solution

How should I solve this problem?

  • Integrate by trigonometric substitution
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • 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

$\int\frac{x^4+3x^2+4}{x+1}dx$

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$\int\frac{x^4+3x^2+4}{x+1}dx$

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Learn how to solve integral calculus problems step by step online. Integrate the function (x^4+3x^2+4)/(x+1). Find the integral. Divide x^4+3x^2+4 by x+1. Resulting polynomial. Expand the integral \int\left(x^{3}-x^{2}+4x-4+\frac{8}{x+1}\right)dx into 5 integrals using the sum rule for integrals, to then solve each integral separately.

Final answer to the problem

$\frac{x^{4}}{4}+\frac{-x^{3}}{3}+2x^2-4x+8\ln\left|x+1\right|+C_0$

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Function Plot

Plotting: $\frac{x^{4}}{4}+\frac{-x^{3}}{3}+2x^2-4x+8\ln\left(x+1\right)+C_0$

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1
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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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