solve pls this question[tex] \implies \pink{ \int \: \frac{x + 2 \: }{ \sqrt{ {x}^{2} + 2x} \: + 3}dx } \\ [/tex]. Created by diwanamrmznu.

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solve pls this question

[tex] \implies \pink{ \int \: \frac{x + 2 \: }{ \sqrt{ {x}^{2} + 2x} \: + 3}dx } \\ [/tex]

Answer:

2√( x² + 2x + 3 ) + c

Step-by-step explanation:

Correct question

∫ ( 2x + 2 ) / √( x² + 2x + 3 ) dx

Let x² + 2x + 3 = y

Differenciate

⇒ ( 2x + 2 ) dx = dy

= ∫ ( 2x + 2 ) √( x² + 2x + 3 ) dx

= ∫ dy / √y

= ∫ y^( - 1/2 ) dy

= y^( - 1/2 + 1 ) / ( - 1/2 + 1 ) + c

= y^( 1/2 ) / ( 1/2 ) + c

= 2√y + c

= 2√( x² + 2x + 3 ) + c