Question

Find the following integrals:
(i) ∫(sin x + cos x) dx
(ii) ∫cosec x (cosec x + cot x) dx​

Answer 1

Solution -

⠀

• ∫(sin x + cos x) dx

We have,

➝ ∫(sin x + cos x) dx

➝ ∫sin x dx + ∫cos x dx

➝ - cos x + sin x + C

⠀

• ∫cosec x (cosec x + cot x) dx

We have,

➝ ∫cosec x (cosec x + cot x) dx

➝ ∫cosec² x dx + ∫cosec x cot x dx

➝ - cot x - cosec x + C

⠀

Integrals used here

• ∫dx = x + C
• ∫cos x dx = sin x + C
• ∫sin x dx = - cos x + C
• ∫cosec² x dx = - cot x + C
• ∫cosec x cot x dx = - cosec x + C

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