Evaluate:∫√x2+2x+5dx

Question

Evaluate:∫√x2+2x+5dx (A) -(1/2)(x+1)√x2+2x+5 +2log |(x+1)+√x2+2x+5 |+C  (B) (1/2)(x+1)√x2+2x+5 +2log |(x+1)+√x2+2x+5 |+C  (C) -(1/2)(x+1)√x2+2x+5 -2log |(x+1)+√x2+2x+5 |+C  (D) None of these

Tardigrade Admin · Accepted Answer

I =∫√x2 + 2x + 5 dx =∫√(x+1)2+(22)dx ⇒ I= (1/2)(x+1)√x2+2x+5 +2log |(x+1)+√x2+2x+5 |+C

Q. Evaluate: $\int x^{2} + 2 x + 5 d x$

$- \frac{1}{2} (x + 1) x^{2} + 2 x + 5 + 2 l o g ∣ ∣ (x + 1) + x^{2} + 2 x + 5 ∣ ∣ + C$

$\frac{1}{2} (x + 1) x^{2} + 2 x + 5 + 2 l o g ∣ ∣ (x + 1) + x^{2} + 2 x + 5 ∣ ∣ + C$

$- \frac{1}{2} (x + 1) x^{2} + 2 x + 5 - 2 l o g ∣ ∣ (x + 1) + x^{2} + 2 x + 5 ∣ ∣ + C$

None of these

$I = \int x^{2} + 2 x + 5 d x = \int (x + 1)^{2} + (2^{2}) d x$

$\Rightarrow I = \frac{1}{2} (x + 1) x^{2} + 2 x + 5 + 2 l o g ∣ ∣ (x + 1) + x^{2} + 2 x + 5 ∣ ∣ + C$

Q. Evaluate:∫x2+2x+5​dx

−21​(x+1)x2+2x+5​+2log∣∣​(x+1)+x2+2x+5​∣∣​+C

21​(x+1)x2+2x+5​+2log∣∣​(x+1)+x2+2x+5​∣∣​+C

−21​(x+1)x2+2x+5​−2log∣∣​(x+1)+x2+2x+5​∣∣​+C