Question

Integration of (3x+4/square root of x²+5x+2)dx

Help....

Answer 1

Step-by-step explanation:

∫

(x+3)

2

e

x

(x

2

+5x+7)

dx

let

u

2

=(x+3)

2

⟹x

2

+5x+7=u

2

−u+1

∫

(u)

2

e

u−3

(u

2

−u+1)

du

=e

−3

∫e

u

(

u

2

1

−

u

1

+1)du

=e

−3

∫e

u

du+e

−3

∫(

u

1

−

u

2

1

)e

u

du

=e

−3

e

u

+

u

e

−3

=e

u−3

+

u

e

−3

Putting the value of u, we get

=e

x

+

x+3

e

−3

+c