Math, asked by mhyadav, 7 months ago


(3+7x) √(9 - 3x ) dx​

Answers

Answered by pulakeshray123
1

Answer:

Solution

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Verified by Toppr

Let I=∫

7x+9

3x+5

dx

Let 3x+5=λ(7x+9)+μ

On equating the coefficeints of like powers of x on both sides, we get

⇒3=7λ⇒λ=

7

3

⇒5=9λ+μ⇒μ=5−9λ=5−9×

7

3

=

7

35−27

=

7

8

Replacing 3x+5 by λ(7x+9)+μ in the given integral, we get

I=∫

7x+9

λ(7x+9)+μ

dx

=∫

7x+9

7

3

(7x+9)+

7

8

dx

=

7

3

7x+9

(7x+9)

dx+

7

8

7x+9

1

dx

=

7

3

∫(7x+9)

1−

2

1

dx+

7

8

∫(7x+9)

2

1

dx

=

7

3

∫(7x+9)

2

1

dx+

7

8

∫(7x+9)

2

1

dx

We know that ∫(ax+b)

n

=

a(n+1)

1

(ax+b)

n+1

=

7

3

×

7

1

2

1

+1

(7x+9)

2

1

+1

+

7

8

×

7

1

2

1

+1

(7x+9)

2

1

+1

+c

=

49

3

2

3

(7x+9)

2

3

+

49

8

2

1

(7x+9)

2

1

+c

=

49

2

(7x+9)

2

3

+

49

16

(7x+9)

2

1

+c

=

49

2

(7x+9)(7x+9)

2

1

+

49

16

(7x+9)

2

1

+c

=

49

2

[(7x+9)+8](7x+9)

2

1

+c

=

49

2

(7x+17)(7x+9)

2

1

+c

Step-by-step explanation:

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