∫√(x^2 + 2x + 5) dx = ∫√(( x + 1 )^2 + 2^2) dx = x + 12√(( x + 1 )^2 + 2^2) + 2^22ln| ( x + 1 ) + √(( x + 1 )^2 + 2^2)| + C = #160;x + 12√ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Standard Formulae - 1

Evaluate: ∫...

Question

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

Open in App

Solution

$\int \sqrt{x^{2} + 2 x + 5} d x$

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

$= \frac{x + 1}{2} \sqrt{{(x + 1)}^{2} + 2^{2}} + \frac{2^{2}}{2} ln ∣ ∣ ∣ (x + 1) + \sqrt{{(x + 1)}^{2} + 2^{2}} ∣ ∣ ∣ + C$

$= \frac{x + 1}{2} \sqrt{{(x + 1)}^{2} + 4} + 2 ln ∣ ∣ ∣ (x + 1) + \sqrt{{(x + 1)}^{2} + 4} ∣ ∣ ∣ + C$

Suggest Corrections

Similar questions

Evaluate the integrals using substitution.
$\int_{- 1}^{1} \frac{1}{x^{2} + 2 x + 5} d x .$

Evaluate the following integral:

\int \frac{2 x - 4}{\sqrt{x^{2} - 4 x - 5}} d x + \int \frac{6}{\sqrt{(x - 2)^{2} - 9}} =

Evaluate $\int x^{2} + 3 x + 5 d x$

\int_{1}^{3} \frac{1}{(x^{2} + 6 x + 5)} d x

\int_{1}^{3} (x^{2} + 6 x + 5) d x

\int \frac{(x^{2} + 1) (x^{2} + 4)}{(x^{2} + 3) (x^{2} - 5)} d x

Join BYJU'S Learning Program