Integration of rational functions, which are quotients of polynomials, is a fundamental concept in calculus. The general form of a rational function is: $$ \frac{P(x)}{Q(x)} $$ where ( P(x) ) and ( Q(x) ) are polynomials. The strategy for integrating such functions typically involves a few steps: (1) Polynomial Division: If the degree of ( […]

Integration of root tan x is little complex. This can be solve using integration by substitution method . The formula is given by $\int \sqrt {tan x} \; dx = \frac {1}{\sqrt 2} \tan^{-1} (\frac {tan x -1}{\sqrt {2tan x}}) + \frac {1}{2\sqrt 2} \ln \frac {(tan x + 1 -\sqrt {2tan x})}{(tan x +

The integration of $sin^7x$, can be found using integration substitution and trigonometry identities . The integral of $\sin^7 x $ with respect to (x) is: \[\int \sin^7 x \, dx =\frac{\cos^7(x)}{7} – \frac{3\cos^5(x)}{5} + \cos^3(x) – \cos(x) + C\] Here, (C) represents the constant of integration, which is added because the process of integration determines

The integral of the sec square function, $\sec ^2x$, can be found using basic calculus principles. The integral of ($\sec ^2x$) with respect to (x) is: \[\int \sec^2 x \, dx = \tan x + C\] Here, (C) represents the constant of integration, which is added because the process of integration determines the antiderivative up

Number 50 is a composite number and we will find how to find the factors of 50. We will also see techniques to find out the Prime factorization of 50 easily Factors of 50 A factor of a number is an exact divisor of that number. So factors of 50 are the numbers which are

Number 32 is a composite number and we will find how to find the factors of 32. We will also see techniques to find out the Prime factorization of 32 easily Factors of 32 A factor of a number is an exact divisor of that number. So factors of 32 are the numbers which are