Evaluate - x-3 - x 2 -4x-3 dx

∫√(x^2+4x+3)dx=∫√((x+2)^2 1) dx=(x+2)2√((x+2)^2 1) 12ln| (x+2)+√((x+2)^2 1) | ∫ (x 3√(x^2+4x+3))dx= x^22 32(x+2)√(x^2+4x+3)+32ln| x+2+√(x^2+4x+3) |+C ...

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

Byju's Answer

Standard XII

Mathematics

Integration by Parts

Evaluate ∫ x...

Question

Evaluate
$\int x - 3 \sqrt{x^{2} + 4 x + 3} d x$

Open in App

Solution

$\int \sqrt{x^{2} + 4 x + 3} d x = \int \sqrt{(x + 2)^{2} - 1} d x = \frac{(x + 2)}{2} \sqrt{(x + 2)^{2} - 1} - \frac{1}{2} ln ∣ (x + 2) + \sqrt{(x + 2)^{2} - 1} ∣$
$\int (x - 3 \sqrt{x^{2} + 4 x + 3}) d x = \frac{x^{2}}{2} - \frac{3}{2} (x + 2) \sqrt{x^{2} + 4 x + 3} + \frac{3}{2} ln ∣ x + 2 + \sqrt{x^{2} + 4 x + 3} ∣ + C$

Suggest Corrections

Similar questions

Q. Evaluate:

\int_{1}^{2} \frac{5 x^{2}}{x^{2} + 4 x + 3} d x

Evaluate the definite integrals.
$\int_{1}^{2} \frac{5 x^{2}}{x^{2} + 4 x + 3} d x$

Q. Evaluate:

\int \frac{2 x + 3}{\sqrt{4 x + 3}} d x =

Q. Evaluate:

\int \frac{x - x^{2}}{x^{2} - 2 x - 3} d x

Q. Evaluate

\int \frac{x}{x^{2} + 3} d x

Join BYJU'S Learning Program

Evaluate∫x−3√x2+4x+3dx

∫√x2+4x+3dx=∫√(x+2)2−1 dx=(x+2)2√(x+2)2−1−12ln∣(x+2)+√(x+2)2−1 ∣∫(x−3√x2+4x+3)dx= x22−32(x+2)√x2+4x+3+32ln∣x+2+√x2+4x+3 ∣+C

Evaluate
$\int x - 3 \sqrt{x^{2} + 4 x + 3} d x$