Part - 1 Lecture - 4 Chapter 7 Integrals
भीड़ हमेशा उस रास्ते पर चलती है जो रास्ता आसान लगता है, लेकिन इसका मतलब यह नहीं की भीड़ हमेशा सही रास्ते पर चलती है|
अपने रास्ते खुद चुनिए क्योंकि आपको आपसे बेहतर और कोई नहीं जानता|
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INTEGRATION OF ALGEBRAIC FUNCTIONS
There are three methods to find the integral of Algebraic functions based on the type of Algebraic function.
FIRST METHOD
The first method is Partial Fractions, used only if the following conditions are satisfying:
• There is no root in either numerator or denominator (Only for rational functions)
• The denominator can be factorised
• It must be a proper fraction. In case of improper fraction, first, convert it into a proper fraction by division method.
| Form of the rational function | Form of partial fraction |
| \(\frac{px+q}{(x-a)(x-b)…(x-z)}\) | \(\frac{A}{(x-a)}+\frac{B}{(x-b)} + … +\frac{Z}{(x-z)}\) |
| \(\frac{px+q}{(x-a)^n}\) | \(\frac{A}{(x-a)}+\frac{B}{(x-a)^2} + … + \frac{Z}{(x-a)^n}\) |
| \(\frac{px^2+qx+r}{(x-a)(x^2+bx+c)}\) | \(\frac{A}{(x-a)} + \frac{Bx+C}{(x^2+bx+c)}\) Where \(x^2+bx+c\) cannot be factorised further… |
In this video, I am discussing one of the three methods of partial fractions.
1. \(\int\frac{dx}{3x^2+13x-10} \)
