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Find the integral $\int\frac{3-x}{2x+1}dx$

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Solution

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Final Answer

$\frac{7}{4}\ln\left(2x+1\right)-\frac{1}{2}x-\frac{1}{4}+C_0$
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Step-by-step Solution

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

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

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

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

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int((3-x)/(2x+1))dx. Expand the fraction \frac{3-x}{2x+1} into 2 simpler fractions with common denominator 2x+1. Simplify the expression inside the integral. The integral \int\frac{3}{2x+1}dx results in: \frac{3}{2}\ln\left(2x+1\right). The integral -\int\frac{x}{2x+1}dx results in: -\frac{1}{4}\left(2x+1\right)+\frac{1}{4}\ln\left(2x+1\right).

Final Answer

$\frac{7}{4}\ln\left(2x+1\right)-\frac{1}{2}x-\frac{1}{4}+C_0$

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 integral of ((3+-1x)/(2x+1))dx using partial fractionsSolve integral of ((3+-1x)/(2x+1))dx using basic integralsSolve integral of ((3+-1x)/(2x+1))dx using u-substitutionSolve integral of ((3+-1x)/(2x+1))dx using integration by partsSolve integral of ((3+-1x)/(2x+1))dx using trigonometric substitution

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Plotting: $\frac{7}{4}\ln\left(2x+1\right)-\frac{1}{2}x-\frac{1}{4}+C_0$

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(◻)
+
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◻/◻
/
÷
◻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: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

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