ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

Find the integral $\int x\left(\frac{3}{x^4}- 6^{\left(-x+1\right)}+\frac{2}{3x-1}\right)dx$

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

$\frac{-3}{2x^{2}}+\frac{6^{\left(-x+1\right)}}{\ln\left|6\right|^2}+\frac{6^{\left(-x+1\right)}x}{\ln\left|6\right|}+\frac{2}{9}\ln\left|3x-1\right|+\frac{2}{3}x+C_1$
Got another answer? Verify it here!

 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
Can't find a method? Tell us so we can add it.
1

Rewrite the integrand $x\left(\frac{3}{x^4}- 6^{\left(-x+1\right)}+\frac{2}{3x-1}\right)$ in expanded form

$\int\left(\frac{3}{x^{3}}-x\cdot 6^{\left(-x+1\right)}+\frac{2x}{3x-1}\right)dx$

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

$\int\left(\frac{3}{x^{3}}-x\cdot 6^{\left(-x+1\right)}+\frac{2x}{3x-1}\right)dx$

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(x(3/(x^4)-6^(-x+1)2/(3x-1)))dx. Rewrite the integrand x\left(\frac{3}{x^4}- 6^{\left(-x+1\right)}+\frac{2}{3x-1}\right) in expanded form. Expand the integral \int\left(\frac{3}{x^{3}}-x\cdot 6^{\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

$\frac{-3}{2x^{2}}+\frac{6^{\left(-x+1\right)}}{\ln\left|6\right|^2}+\frac{6^{\left(-x+1\right)}x}{\ln\left|6\right|}+\frac{2}{9}\ln\left|3x-1\right|+\frac{2}{3}x+C_1$

 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

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

 Main Topic: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.