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# Find the integral $\int x\left(\frac{3}{x^4}- 3^{\left(-x+1\right)}+\frac{2}{3x-1}\right)dx$

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##  Final answer to the problem

$\frac{-3}{2x^{2}}+\frac{3^{\left(-x+1\right)}}{\ln\left|3\right|^2}+\frac{3^{\left(-x+1\right)}x}{\ln\left|3\right|}+\frac{2}{9}\ln\left|3x-1\right|+\frac{2}{3}x+C_1$
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##  Step-by-step Solution 

How should I solve this problem?

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

Rewrite the integrand $x\left(\frac{3}{x^4}- 3^{\left(-x+1\right)}+\frac{2}{3x-1}\right)$ in expanded form

$\int\left(\frac{3}{x^{3}}-x\cdot 3^{\left(-x+1\right)}+\frac{2x}{3x-1}\right)dx$

Learn how to solve problems step by step online.

$\int\left(\frac{3}{x^{3}}-x\cdot 3^{\left(-x+1\right)}+\frac{2x}{3x-1}\right)dx$

Learn how to solve problems step by step online. Find the integral int(x(3/(x^4)-3^(-x+1)2/(3x-1)))dx. Rewrite the integrand x\left(\frac{3}{x^4}- 3^{\left(-x+1\right)}+\frac{2}{3x-1}\right) in expanded form. Expand the integral \int\left(\frac{3}{x^{3}}-x\cdot 3^{\left(-x+1\right)}+\frac{2x}{3x-1}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. Take out the constant 2 from the integral. The integral \int\frac{3}{x^{3}}dx results in: \frac{-3}{2x^{2}}.

##  Final answer to the problem

$\frac{-3}{2x^{2}}+\frac{3^{\left(-x+1\right)}}{\ln\left|3\right|^2}+\frac{3^{\left(-x+1\right)}x}{\ln\left|3\right|}+\frac{2}{9}\ln\left|3x-1\right|+\frac{2}{3}x+C_1$

##  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

SnapXam A2

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0
a
b
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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