For, x 2 ≠ n π + 1 ,   n ∈ N (the set of natural numbers), the integral ∫ x 2 sin x 2 - 1 - sin 2 x 2 - 1 2 sin x 2 - 1 + sin 2 x 2 - 1 d x , is equal to (where c is a constant of integration).

Question

For, x 2 &#8800; n &#960; + 1 , &#160; n &#8712; N (the set of natural numbers), the integral &#8747; x 2 sin x 2 - 1 - sin 2 x 2 - 1 2 sin x 2 - 1 + sin 2 x 2 - 1 d x , is equal to (where c is a constant of integration).

Aicharya · Accepted Answer

&#8658; I = &#8747; x 2 s i n x 2 - 1 - s i n 2 x 2 - 1 2 s i n x 2 - 1 + s i n 2 x 2 - 1 d x Let, x 2 - 1 = &#952; &#8658; x d x = 1 2 d &#952; &#8658; I = 1 2 &#8747; 2 s i n &#952; - s i n 2 &#952; 2 s i n &#952; + s i n 2 &#952; d &#952; = 1 2 &#8747; 2 s i n &#952; - 2 s i n &#952; c o s &#952; 2 s i n &#952; + 2 s i n &#952; c o s &#952; d &#952; = 1 2 &#8747; 1 - c o s &#952; 1 + c o s &#952; d &#952; = 1 2 &#8747; t a n &#952; 2 d &#952; = 1 2 log e sec &#952; 2 1 2 + c , where c is the constant of integration. = log e sec 2 x 2 - 1 2 + c

For, x 2 ≠ n π + 1 ,   n ∈ N (the set of natural numbers), the integral ∫ x 2…

Solution

For, x 2 &#8800; n &#960; + 1 , &#160; n &#8712; N (the set of natural numbers), the integral &#8747; x 2…

Solution

For, x 2 ≠ n π + 1 , n ∈ N (the set of natural numbers), the integral ∫ x 2…