What is the antiderivative of Cscx?
What is the antiderivative of Cscx?
Calculus Examples The integral of csc(x) with respect to x is ln(|csc(x)−cot(x)|) ln ( | csc ( x ) – cot ( x ) | ) . The answer is the antiderivative of the function f(x)=csc(x) f ( x ) = csc ( x ) .
How is the integral of Cscx derived?
Here are the formulas of integral of csc x with the respective methods of proving them.
- Using the substitution method, ∫ csc x dx = ln |csc x – cot x| + C (or)
- Using partial fractions, ∫ csc x dx = (1/2) ln | (cos x – 1) / (cos x + 1) | + C.
- Using trigonometric formulas, ∫ csc x dx = ln | tan (x/2) | + C.
What is the derivative of csc?
The double derivative of csc x is csc x (cot2x + csc2x). The double derivative is nothing but the second derivative of a function which can be obtained by differentiating the first derivative of csc x.
What is the antiderivative of TANX?
Integral tan(x) tan x = – ln|cos x| + C.
What is the derivative of Cscx 2?
Using the chain rule, the derivative of csc^2x is -2.csc^2(x).cot(x)
| csc2x | ► Derivative of csc2x = -2csc2(x)cot(x) |
|---|---|
| csc 2 x | ► Derivative of csc 2 x = -2csc2(x)cot(x) |
| (cscx)^2 | ► Derivative of (cscx)^2 = -2csc2(x)cot(x) |
| csc squared x | ► Derivative of csc squared x = -2csc2(x)cot(x) |
| cscx2 | ► Derivative of cscx2 = -2csc2(x)cot(x) |
How do you find the derivative of csc 2x?
We know how to differentiate csc(x) (the answer is -csc(x)cot(x))…Using the chain rule to find the derivative of csc(2x)
| csc2x | ► Derivative of csc2x = -2cot(2x)csc(2x) |
|---|---|
| csc 2 x | ► Derivative of csc 2 x = -2cot(2x)csc(2x) |
What is the antiderivative of tan 2x?
The answer is: tanx−x+c . =∫(tan2x+1)dx−∫dx=tanx−x+c .
What is the antiderivative of csc 2x?
Combine 12 1 2 and ln(|csc(u)−cot(u)|) ln ( | csc ( u ) – cot ( u ) | ) . Replace all occurrences of u with 2x . The answer is the antiderivative of the function f(x)=csc(2x) f ( x ) = csc ( 2 x ) .
