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Find the integral of $\frac{x+1}{4-x}$

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Solution

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Final Answer

$-5\ln\left(4-x\right)-x+C_1$
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Step-by-step Solution

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Find the integral

$\int\frac{x+1}{4-x}dx$

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$\int\frac{x+1}{4-x}dx$

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

Final Answer

$-5\ln\left(4-x\right)-x+C_1$

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

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

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Plotting: $-5\ln\left(4-x\right)-x+C_1$

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0
a
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f
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m
n
u
v
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x
y
z
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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: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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