23. integrate
dx by
1-sin x
Answers
Answered by
3
EXPLANATION.
⇒ ∫dx/1 - sin(x).
As we know that,
Rationalize the equation, we get.
⇒ ∫dx/1 - sin(x) x (1 + sin(x))/(1 + sin(x)).
⇒ ∫(1 + sin x)dx/(1 - sin²x).
⇒ ∫(1 + sin x)dx/cos²x.
⇒ ∫dx/cos²x + ∫sin x/cos²x dx.
⇒ ∫sec²xdx + ∫tan x . sec x dx.
⇒ tan(x) + sec(x) + c.
MORE INFORMATION.
Standard integrals.
(1) = ∫sin x dx = - cos x + c.
(2) = ∫cos x dx = sin x + c.
(3) = ∫tan x dx = ㏒(sec x) + c = -㏒(cos x) + c.
(4) = ∫cot x dx = ㏒(sin x) + c.
(5) = ∫sec x dx = ㏒(sec x + tan x) + c = ㏒ tan(π/4 + x/2) + c.
(6) = ∫cosec x dx = -㏒(cosec x + cot x) + c = ㏒(cosec x - cot x) + c = ㏒ tan(x/2) + c.
(7) = ∫sec x tan x dx = sec x + c.
(8) = ∫cosec x cot x dx = - cosec x + c.
(9) = ∫sec²xdx = tan x + c.
(10) = ∫cosec²dx = - cot x + c.
Similar questions
English,
1 month ago
Math,
1 month ago
Science,
2 months ago
CBSE BOARD X,
2 months ago
Science,
9 months ago
Social Sciences,
9 months ago