What is the antiderivative of arcsin?

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What is the antiderivative of arcsin?

Mathematically, the sin inverse integral is written as ∫arcsin x dx = ∫sin-1x dx = x sin-1x + √(1 – x2) + C. Integral of sin inverse x is also called the antiderivative of sin inverse x.

How do you integrate arcsec?

1 Answer

  1. Method: To integrate arcsec(x) , substitution, then integrate by parts.
  2. You’ll also need ∫secudu , which can be done by substitution and partial fractions.
  3. Details: ∫arcsec(x)dx.
  4. Let y=arcsec(x) , so x=secy and dx=secytanydy .
  5. ∫ysecytanydy .
  6. Integrate this by parts:
  7. uv−∫vdu=ysecy−∫secydy.

How do you find the derivative of arcsin 2x?

Explanation: Use chain rule to find the derivative. The derivative of arcsin x is 1/square root of 1-x^2 and then multiply by the derivative of 2x.

What is the formula for arcsin?

arcsin(x) = π/2 – arccos(x)

What are the integration rules?

Integration Rules

Common Functions Function Integral
Power Rule (n≠−1) ∫xn dx xn+1n+1 + C
Sum Rule ∫(f + g) dx ∫f dx + ∫g dx
Difference Rule ∫(f – g) dx ∫f dx – ∫g dx
Integration by Parts See Integration by Parts

What is arctan integral?

The integral of arctan is the integration of tan inverse x, which is also called the antiderivative of arctan, which is given by ∫tan-1x dx = x tan-1x – ½ ln |1+x2| + C, where C is the constant of integration. The integral of arctan can be calculated using the integration by parts method.

What does arcsec mean?

1⁄3600 of a degree of an angle.

What is the antiderivative of arctan?

The integral of arctan is the integration of tan inverse x, which is also called the antiderivative of arctan, which is given by ∫tan-1x dx = x tan-1x – ½ ln |1+x2| + C, where C is the constant of integration.

What is the arcsin of 2?

As a Real valued function arcsin2 is undefined, since sin(x)∈[−1,1] for all x∈R .

How do you find arcsin?

How to calculate antiderivative?

Separate the integrals:∫cos x+x dx =∫cos x dx+∫x dx

  • Find the individual solutions:
  • ∫cos x = sin x
  • ∫x = = sin x+x 2/2+C (see: power function integration rule)

    • How do I find the most general antiderivative?

    If F is an antiderivative of f,then every antiderivative of f is of the form F(x)+C for some constant C.

  • Solving the initial-value problem dy dx = f(x),y(x0) = y0
  • requires us first to find the set of antiderivatives of f and then to look for the particular antiderivative that also satisfies the initial condition.

    • How to find the most general antiderivative?

    Find the general antiderivative of a given function.

  • Explain the terms and notation used for an indefinite integral.
  • State the power rule for integrals.
  • Use antidifferentiation to solve simple initial-value problems.

    • How do you find the antiderivative?

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