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Find the integral $\int\frac{5x+1}{\left(2x+1\right)\left(x-1\right)}dx$

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Solution

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Final answer to the problem

$\frac{1}{2}\ln\left|2x+1\right|+2\ln\left|x-1\right|+C_0$
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Step-by-step Solution

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  • 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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Rewrite the fraction $\frac{5x+1}{\left(2x+1\right)\left(x-1\right)}$ in $2$ simpler fractions using partial fraction decomposition

Learn how to solve differential calculus problems step by step online.

$\frac{1}{2x+1}+\frac{2}{x-1}$

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Learn how to solve differential calculus problems step by step online. Find the integral int((5x+1)/((2x+1)(x-1)))dx. Rewrite the fraction \frac{5x+1}{\left(2x+1\right)\left(x-1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{2x+1}+\frac{2}{x-1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{2x+1}dx results in: \frac{1}{2}\ln\left(2x+1\right). The integral \int\frac{2}{x-1}dx results in: 2\ln\left(x-1\right).

Final answer to the problem

$\frac{1}{2}\ln\left|2x+1\right|+2\ln\left|x-1\right|+C_0$

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Function Plot

Plotting: $\frac{1}{2}\ln\left(2x+1\right)+2\ln\left(x-1\right)+C_0$

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0
a
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n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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

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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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