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vodka [1.7K]
3 years ago
10

Find the following integral. Integrate x + 5/x^2 +10x +26 dx

Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
6 0

Given :

Polynomial , f(x)=x+\dfrac{5}{x^2}+10x+26 .

To Find :

Integration of f(x) .

Solution :

We know , integration of x^n is :

\int x^n \, dx = \dfrac{x^{n+1}}{n+1}+C

( Here , is C is a constant )

Now ,

\int f(x)\ dx=\int( x+\dfrac{5}{x^2}+10x+26)dx\\                  \\                 \int f(x)\ dx= \int x\ dx+\int 5x^{-2}\ dx+\int 10 x \ dx +26\ dx\\                 \\                 \int f(x)\ dx=\dfrac{x^2}{2}+\dfrac{5\times x^{-1}}{(-1)}+\dfrac{10x^2}{2}+26x+C\\\\                 \int f(x)\ dx=\dfrac{11x^2}{2}+26x-5x^{-1}+C

Therefore , the integration is \dfrac{11x^2}{2}+26x-5x^{-1}+C .

Hence , this is the required solution .

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Step-by-step explanation:

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46 + angle C = 110

angle C = 110 - 46

angle C = 64 degree

In triangle ABC

finding angle B

angle A + angle B + angle C = 180 degree (sum of interior angles of a triangle)

78 + angle B + 64 = 180

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3 years ago
Tanh(2a)==1/2 then a=?​
stepladder [879]

Answer:

2a=1/2

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Step-by-step explanation:

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2 years ago
Martin deposits $200 in a savings account that earns 5% annual interest. four years later, cary deposits $200 in an account earn
Scrat [10]
<span>Martin deposits $200 in a savings account that earns 5% annual interest.

year         interest                       balance

1              200 * 5%                    200(1.05)

2              200(1.05) * 5%          200(1.05)^2

3              200(1.05)^2*5%        200(1.05)^3

y                                                200(1.05)^y

=> m = 200 (1.05)^y

four years later, cary deposits $200 in an account earning the same interest.

</span>
<span><span>year         interest                       balance

5              200 * 5%                    200(1.05)

6              200(1.05) * 5%          200(1.05)^2

7             200(1.05)^2*5%        200(1.05)^3

y                                                200(1.05)^(y-4)

=> c = 200(1.05)^ (y-4)
</span>
Answer:
Martin: 200(1.05)^y
Cary: 200(1.05)^(y–4)
</span>
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3 years ago
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LenKa [72]

Answer:

2

Step-by-step explanation:

The constant of proportionality in the equation x/y = 2/g is 2. 2 is the only number in the equation.

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4(PX+1)=64 what is the value of x in terms of p and what is the value of x when p is -5 ?
Oksana_A [137]

Answer:

x = -3

Step-by-step explanation:

4(PX+1)=64\\\\p= -5

Substitute -5 for p in the given equation and solve

4(-5(x)+1)=64\\\\\mathrm{Divide\:both\:sides\:by\:}4\\\frac{4\left(-5x+1\right)}{4}=\frac{64}{4}\\\\Simplify\\-5x+1=16\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\-5x+1-1=16-1\\\\Simplify\\-5x =15\\\\\mathrm{Divide\:both\:sides\:by\:}-5\\\frac{-5x}{-5}=\frac{15}{-5}\\\\Simplify\\x = -3

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2 years ago
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