Integrate the function $a^4-4a^2-4a+\frac{-1}{a^2}+2a+1$

Step-by-step Solution

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Final answer to the problem

$\frac{a^{5}}{5}-\frac{4}{3}a^{3}-a^2+\frac{1}{a}+a+C_0$
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Step-by-step Solution

How should I solve this problem?

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

Find the integral

$\int\left(a^4-4a^2-4a+\frac{-1}{a^2}+2a+1\right)da$

Learn how to solve integrals of rational functions problems step by step online.

$\int\left(a^4-4a^2-4a+\frac{-1}{a^2}+2a+1\right)da$

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Unlock the first 3 steps of this solution

Learn how to solve integrals of rational functions problems step by step online. Integrate the function a^4-4a^2-4a-1/(a^2)2a+1. Find the integral. Simplify the expression. The integral \int a^4da results in: \frac{a^{5}}{5}. The integral \int-4a^2da results in: -\frac{4}{3}a^{3}.

Final answer to the problem

$\frac{a^{5}}{5}-\frac{4}{3}a^{3}-a^2+\frac{1}{a}+a+C_0$

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Function Plot

Plotting: $\frac{a^{5}}{5}-\frac{4}{3}a^{3}-a^2+\frac{1}{a}+a+C_0$

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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: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

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