The value of ∫(dx/√(3-5x-x2)) is

Question

The value of ∫(dx/√(3-5x-x2)) is (A)  sin -1( (2x+5/√37) )+c  (B)  sinh -1( (2x+5/√37) )+c  (C)  sin -1( (2x+5/37) )+c  (D) None of the above

Tardigrade Admin · Accepted Answer

∫(dx/√(3-5x-x2)) =∫(dx/√-[ x2+5x-3+( (5)2 )2-( (5)2 )2 ] =∫(dx/√-[ ( x+(5)2 )2-(37)4 ] =∫(dx/√( (√37)2 )2-( x+(5)2 )2 =/ sin )/-1)[ (( x+(5/2) )/( (√37)2 )) ]+c =/ sin )-1[ (2x+5/√37) ]+c

Q. The value of $\int \frac{d x}{( 3 - 5 x - x ^{2} )}$ is

$sin^{- 1} (\frac{2 x + 5}{37}) + c$

$sinh^{- 1} (\frac{2 x + 5}{37}) + c$

$sin^{- 1} (\frac{2 x + 5}{37}) + c$

None of the above

Q. The value of ∫(3−5x−x2)​dx​ is

sin−1(37​2x+5​)+c

sinh−1(37​2x+5​)+c

sin−1(372x+5​)+c

None of the above

∫(3−5x−x2)​dx​ =∫−[x2+5x−3+(25​)2−(25​)2]​dx​ =∫−[(x+25​)2−437​]​dx​ =∫(237​​)2−(x+25​)2​dx​ =sin−1[(237​​)(x+25​)​]+c =sin−1[37​2x+5​]+c

Q. The value of $\int \frac{d x}{( 3 - 5 x - x ^{2} )}$ is

$sin^{- 1} (\frac{2 x + 5}{37}) + c$

$sinh^{- 1} (\frac{2 x + 5}{37}) + c$

$sin^{- 1} (\frac{2 x + 5}{37}) + c$