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[tex] \implies \pink{ \int \: \frac{x + 2 \: }{ \sqrt{ {x}^{2} + 2x} \: + 3}dx } \\ [/tex]
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solve pls this question
[tex] \implies \pink{ \int \: \frac{x + 2 \: }{ \sqrt{ {x}^{2} + 2x} \: + 3}dx } \\ [/tex]
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Verified answer
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