👉 Try now NerdPal! Our new math app on iOS and Android

Integrate the function $\frac{-x^4-22x^3+134x^2+280x-996}{x^5-3x^4-23x^3+51x^2+94x-120}$

Step-by-step Solution

Go!
Symbolic mode
Text mode
Go!
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

Final answer to the problem

$-\frac{121}{24}\ln\left(x-1\right)-\frac{75}{28}\ln\left(x-3\right)+\frac{118}{63}\ln\left(x+4\right)+0.7519841\ln\left(x-5\right)+\frac{86}{21}\ln\left(x+2\right)+C_0$
Got another answer? Verify it here!

Step-by-step Solution

How should I solve this problem?

  • Integrate using trigonometric identities
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
  • Load more...
Can't find a method? Tell us so we can add it.
1

Find the integral

$\int\frac{-x^4-22x^3+134x^2+280x-996}{x^5-3x^4-23x^3+51x^2+94x-120}dx$

Learn how to solve problems step by step online.

$\int\frac{-x^4-22x^3+134x^2+280x-996}{x^5-3x^4-23x^3+51x^2+94x-120}dx$

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution.

Learn how to solve problems step by step online. Integrate the function (-x^4-22x^3134x^2280x+-996)/(x^5-3x^4-23x^351x^294x+-120). Find the integral. Rewrite the expression \frac{-x^4-22x^3+134x^2+280x-996}{x^5-3x^4-23x^3+51x^2+94x-120} inside the integral in factored form. Rewrite the fraction \frac{-x^4-22x^3+134x^2+280x-996}{\left(x-1\right)\left(x-3\right)\left(x+4\right)\left(x-5\right)\left(x+2\right)} in 5 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C, D, F. The first step is to multiply both sides of the equation from the previous step by \left(x-1\right)\left(x-3\right)\left(x+4\right)\left(x-5\right)\left(x+2\right).

Final answer to the problem

$-\frac{121}{24}\ln\left(x-1\right)-\frac{75}{28}\ln\left(x-3\right)+\frac{118}{63}\ln\left(x+4\right)+0.7519841\ln\left(x-5\right)+\frac{86}{21}\ln\left(x+2\right)+C_0$

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

Give us your feedback!

Function Plot

Plotting: $-\frac{121}{24}\ln\left(x-1\right)-\frac{75}{28}\ln\left(x-3\right)+\frac{118}{63}\ln\left(x+4\right)+0.7519841\ln\left(x-5\right)+\frac{86}{21}\ln\left(x+2\right)+C_0$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

Go!
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:

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Unlimited step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account