# Evaluate: <

Let I =

cos 2x = 2cos2 x – 1 and cos 2α = 2cos2 α – 1

I =

I =

As, a2 – b2 = (a+b)(a-b)

I =

I =

I =

I = 2 sin x + 2 cos α

I = 2(sin x + x cos α) + C

OR

Let, I =

I =

I =

Let, I1 = and I2 =

I = I1 + I2 …(1)

First we will calculate I1 and I2 and then add both to get the answer.

Calculation of I1 :

Let x2 + 2x + 3 = u

du = 2(x + 1)dx

(x + 1)dx = du/2

I1 =

I1 = + C1

I1 = ...(2)

Calculation of I2 :

I2 =

I2 =

Use the formula:

I2 =

I2 = …(3)

from equation 1, 2 and 3 we have –

I =

I =

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