Evaluate: `int(3\ s in\ x-2cosx+4s e c^2x-5cos e c^2x)\ dx` (ii) `intsqrt(1+cos2x)\ dx`

Explanation

Solution:

(i)

`\Rightarrow \int 3 \sin x d x-\int 2 \cos x d x+\int 4 \sec ^{2} x d x-\int 5 {cosec}^{2} x d x`

`\Rightarrow 3 \int \sin x d x-2 \int \cos x d x+4 \int \sec ^{2} x d x-5 \int {cosec}^{2} x d x`

`\Rightarrow 3(-\cos x)-2(\sin x)+4(\tan x)-5(\cot x)+C `

`\Rightarrow-3 \cos x-2 \sin x+4 \tan x-5 \cot x+C .`

(ii)

`\Rightarrow \int \sqrt{1+(2 \cos ^{2} x-1)} d x `

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