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3 years ago

3-(x-1)=-1-(5-x) pls help

Mathematics

1 answer:

Alika [10]3 years ago

3 0

Answer:

$- 3(x - 1) = - 1(5 - x) \\ \\ 3 - x + 1 = - 5 + x \\ \\ - x - x = - 5 - 3 - 1 \\ \\ - 2x = - 5 - 3 - 1 \\ \\ - 2x = - 9 \\ \\ x = \frac{ - 9}{ - 2} \\ \\ x = 4.5$

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Please help me do it

Lana71 [14]

Step-by-step Explanation:

We are going to solve this problem using integration by parts. We can write the integrand as

$\dfrac{4x}{x^2+4x+3} = \dfrac{4x}{(x+3)(x+1)}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:= \dfrac{A}{x+3} + \dfrac{B}{x+1}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:= \dfrac{Ax + A + Bx + 3B}{x^2+4x+3}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:=\dfrac{(A+B)x + (A+3B)}{x^2+4x+3}$

Comparing the above term to the left hand side, we can see that

(A + B)x = 4x

A + 3B = 0

Solving for A and B, we find that A = 6 and B = -2 so our integrand becomes

$\dfrac{4x}{x^2+4x+3} = \dfrac{6}{x+3} - \dfrac{2}{x+1}$

We can now easily integrate this expression as follows:

$\displaystyle \int{\dfrac{4x}{x^2+4x+3}}dx = 6\int{\dfrac{dx}{x+3}} - 2\int{\dfrac{dx}{x+1}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:= 6\ln|x+3| - 2\ln|x+1| + C$

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Answer:

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Step-by-step explanation:

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