What is integral of cosec X?

The integral of cosec x is denoted by ∫ cosec x dx (or) ∫ csc x dx and its value is ln |cosec x – cot x| + C. This is also known as the antiderivative of cosec x. ∫ cosec x dx = – ln |cosec x + cot x| + C [OR] ∫ cosec x dx = (1/2) ln | (cos x – 1) / (cos x + 1) | + C [OR] ∫ cosec x dx = ln | tan (x/2) | + C.

What is integral of tan x?

The integral of tan x is ln|cos x| + C .

What is integral of ln x?

We see that the integral of ln(x) is xln(x) – x + C.

What is the antiderivative of sec x tan x?

What is the Anti-derivative of Sec x Tan x? The anti-derivative of sec x tan x is equal to sec x + C, where C is the constant of integration.

What is SEC cosec cot?

Secant (sec) is the reciprocal of cosine (cos) Cosecant (cosec) is the reciprocal of sin. Cotangent (cot) is the reciprocal of tan.

What is the antiderivative of Tan SEC?

Since the derivative of sec(x) is sec(x)⋅tan(x) sec ( x ) ⋅ tan ( x ) , the integral of sec(x)⋅tan(x) sec ( x ) ⋅ tan ( x ) is sec(x) . The answer is the antiderivative of the function f(x)=sec(x)⋅tan(x) f ( x ) = sec ( x ) ⋅ tan ( x ) .

How do you integrate cosec^2x?

Integrate cosec^2x To integrate cosec^2x, also written as ∫cosec 2 x dx, cosec squared x, cosec^2 (x), and (cosec x)^2, we start by using standard trig identities to simplify the integral. We recall the standard trig identity for cosecx, and square both sides. We divide the numerator and denominator by cos squared x.

What are the integrals for tan x and sec x?

The integrals for tan x and sec x are from standard formula. They are ln (cos x) and ln (sec x + tan x), respectively. Combine them to get the following result: The real part is zero, which agrees with at least 2 other answerers.

How to integrate sec2x + secxtanx + Tanx?

Integrating the secant requires a bit of manipulation. Multiply secx by secx +tanx secx +tanx, which is really the same as multiplying by 1. Thus, we have. ∫( secx(secx +tanx) secx +tanx)dx. ∫ sec2x + secxtanx secx + tanx dx. Now, make the following substitution: u = secx +tanx. du = (secxtanx +sec2x)dx = (sec2x + secxtanx)dx.

What is the integral of cscx – cscxcotx?

u = cscx −cotx ⇒ du dx = −cscxcotx + csc2x, And so our integral becomes: ∫ cscx dx = ∫ 1 u du = ln|u| + C