Question

integrate:x/√2x^2+3
​

Answer 1

Question:-

• Integrate.

Solution:-

$\displaystyle \int \sf \small \frac{x}{ \sqrt{2 {x}^{2} + 3 } } \: dx$

Using substitution, $\sf t=\sqrt{2x^{2}+3}$, we get,

$\displaystyle = \int \sf \small \frac{1}{2} dt$

Using $\displaystyle \int \sf a \: dx = a \times x$

We get,

$\sf = \frac{1}{2} \times \sqrt{2 {x}^{2} + 3 }$

Now, add the constant of integration,

$\sf = \frac{1}{2} \times \sqrt{2 {x}^{2} + 3 } + C, C\in R$

Answer:-

• $\sf \frac{1}{2} \times \sqrt{2 {x}^{2} + 3 } + C, C\in R$

Answer 2

Answer:

Question:-

Integrate.

Solution:-

\displaystyle \int \sf \small \frac{x}{ \sqrt{2 {x}^{2} + 3 } } \: dx∫

2x

2

+3

x

dx

Using substitution, \sf t=\sqrt{2x^{2}+3}t=

2x

2

+3

, we get,

\displaystyle = \int \sf \small \frac{1}{2} dt=∫

2

1

dt

Using \displaystyle \int \sf a \: dx = a \times x∫adx=a×x

We get,

\sf = \frac{1}{2} \times \sqrt{2 {x}^{2} + 3 }=

2

1

×

2x

2

+3

Now, add the constant of integration,

\sf = \frac{1}{2} \times \sqrt{2 {x}^{2} + 3 } + C, C\in R=

2

1

×

2x

2

+3

+C,C∈R

Answer:-

\sf \frac{1}{2} \times \sqrt{2 {x}^{2} + 3 } + C, C\in R

2

1

×

2x

2

+3

+C,C∈R

hoe the answer helps u