(4x+2){x²+x+1} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.2
Integrate the functions in Exercises 23 to 59.

Question : 31 of 271

Marks: +1, -0

(4x+2)\sqrt{x^2+x+1}

Solution:

Let

I=\int (4x+2)\sqrt{x^2+x+1}dx

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

Put

x^2 + x + 1 = t

\Rightarrow (2x+1)dx = dt

I=2\int \sqrt{t}dt = \frac{2t^{3/2}}{3/2}+C

=\frac{4}{3}t^{3/2}+C

=\frac{4}{3}(x^2 + x + 1)^{3/2}+C

Go to Question: