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# Find the integral $\int\frac{x^3+1}{x^4}dx$

## Step-by-step Solution

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$\ln\left(x\right)+\frac{1}{-3x^{3}}+C_0$
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##  Step-by-step Solution 

Problem to solve:

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

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Expand the fraction $\frac{x^3+1}{x^4}$ into $2$ simpler fractions with common denominator $x^4$

$\int\left(\frac{x^3}{x^4}+\frac{1}{x^4}\right)dx$

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

$\int\left(\frac{x^3}{x^4}+\frac{1}{x^4}\right)dx$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^3+1)/(x^4))dx. Expand the fraction \frac{x^3+1}{x^4} into 2 simpler fractions with common denominator x^4. Simplify the resulting fractions. Expand the integral \int\left(\frac{1}{x}+\frac{1}{x^4}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{x}dx results in: \ln\left(x\right).

$\ln\left(x\right)+\frac{1}{-3x^{3}}+C_0$

##  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

Solve int((x^3+1)/(x^4))dx using partial fractionsSolve int((x^3+1)/(x^4))dx using basic integralsSolve int((x^3+1)/(x^4))dx using u-substitutionSolve int((x^3+1)/(x^4))dx using integration by partsSolve int((x^3+1)/(x^4))dx using trigonometric substitution

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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

### Main topic:

Integrals of Rational Functions

~ 0.07 s

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