Question

find the integral of 2x+3/5x2+1​

Answer 1

Answer:

∫

5x

2

+1

2x+3

dx

=

5

1

∫

5x

2

+1

10x+15

dx

=

5

1

∫

5x

2

+1

10x

dx+3∫

5x

2

+1

dx

=

5

1

∫

5x

2

+1

10x

dx+

5

3

∫

x

2

+

5

1

dx

putting 5x

2

+1=t

10xdx=dt

=

5

1

∫

t

dt

+

5

3

∫

x

2

+(

5

1

)

2

dx

=

5

1

log∣t∣+

5

3

×

(

5

1

)

1

tan

−1

(

5

1

)

x

+c

=

5

1

log

∣

∣

∣

5x

2

+1

∣

∣

∣

+

5

3

5

tan

−1

(

5

x)+c

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Answer 2

Answer:

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