Maths

Integration of tan inverse x can be calculated using integration by parts .Here is the formula for it \[ \int \tan^{-1}x \, dx = x \tan^{-1}x – \frac {1}{2} \ln (1 + x^2) + C \] where (C) is the constant of integration. Proof of integration of tan inverse x To find the integral we […]

Integration of cos inverse x can be calculated using integration by parts ,integration by substitution .Here is the formula for it \[ \int \cos^{-1}x \, dx = x \cos^{-1}x – \sqrt{1 – x^2} + C \] where (C) is the constant of integration. Proof of integration of cos inverse x We can prove it using

Integration of sin inverse x can be calculated using integration by parts ,integration by substitution .Here is the formula for it \[ \int \sin^{-1}x \, dx = x \sin^{-1}x + \sqrt{1 – x^2} + C \] where (C) is the constant of integration. Proof of integration of sin inverse x We can prove it using

Integration of fractional part of x For example, to integrate the fractional part function from a to b, where a and b are real numbers and a < b, you would do the following: For a general formula, if a and b are not integers, you would need to calculate the integrals over the first

Integrating a constant is a fundamental concept in calculus. When you integrate a constant ( c ) with respect to a variable ( x ), the result is a linear function in ( x ). The integration is performed as follows: $$ \int c \, dx = c \cdot x + C $$ Here, (