Class 12th Integrals of Some Particular Functions NCERT Class 12 Notes Maths Maths Integrals NCERT Class 12 Maths

Where do I find the Integration of a particular function Formula?

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Vikash Kumar Vishwakarma | Contributor-Level 7

a month ago

Students can find the formula of integration for a particular function in this article. It is important to memorise these formulas to solve the integral problem easily. Below is the integration of a particular function formula.

The formula of a particular function:

1. Power Rule:

$\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C (n \neq - 1)$

2. Reciprocal Function:

$\int \frac{1}{x} d x = ln | x | + C$

3. Trigonometric Function:

$\int sin x d x = - cos x + C$
$\int cos x d x = sin x + C$
$\int {sec}^{2} x d x = tan x + C$
$\int {csc}^{2} x d x = - cot x + C$
$\int sec x tan x d x = sec x + C$
$\int csc x cot x d x = - csc x + C$

4. Inverse Trigonometric Function

$\int \frac{1}{1 + x^{2}} d x = {tan}^{- 1} x + C$
$\int \frac{1}{\sqrt{1 - x^{2}}} d x = {sin}^{- 1} x + C$
$\int \frac{- 1}{\sqrt{1 - x^{2}}} d x = {cos}^{- 1} x + C$

Students can find the formula of integration for a particular function in this article. It is important to memorise these formulas to solve the <a href="https://www.shiksha.com/preparation/maths-integrals-integration-2739-tp">integral</a> problem easily. Below is the integration of a particular function formula.The formula of a particular function:1. Power Rule:  <math> <mo>∫</mo> <msup> <mi>x</mi> <mi>n</mi> </msup> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mfrac> <msup> <mi>x</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mo>+</mo> <mi>C</mi> <mspace width="1em"></mspace> <mo>(</mo> <mi>n</mi> <mo>≠</mo> <mo>−</mo> <mn>1</mn> <mo>)</mo> </math> 2. Reciprocal Function: <math > <mo>∫</mo> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>ln</mo> <mo>|</mo> <mi>x</mi> <mo>|</mo> <mo>+</mo> <mi>C</mi> </math> 3. Trigonometric Function: <ul><li> <math > <mo>∫</mo> <mo>sin</mo> <mspace width="0.2em"></mspace> <mi>x</mi> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mo>cos</mo> <mspace width="0.2em"></mspace> <mi>x</mi> <mo>+</mo> <mi>C</mi> </math> </li><li> <math > <mo>∫</mo> <mo>cos</mo> <mspace width="0.2em"></mspace> <mi>x</mi> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>sin</mo> <mspace width="0.2em"></mspace> <mi>x</mi> <mo>+</mo> <mi>C</mi> </math> </li><li> <math > <mo>∫</mo> <msup> <mo>sec</mo> <mn>2</mn> </msup> <mspace width="0.2em"></mspace> <mi>x</mi> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>tan</mo> <mspace width="0.2em"></mspace> <mi>x</mi> <mo>+</mo> <mi>C</mi> </math> </li><li> <math > <mo>∫</mo> <msup> <mo>csc</mo> <mn>2</mn> </msup> <mspace width="0.2em"></mspace> <mi>x</mi> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mo>cot</mo> <mspace width="0.2em"></mspace> <mi>x</mi> <mo>+</mo> <mi>C</mi> </math> </li><li> <math > <mo>∫</mo> <mo>sec</mo> <mspace width="0.2em"></mspace> <mi>x</mi> <mo>tan</mo> <mspace width="0.2em"></mspace> <mi>x</mi> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>sec</mo> <mspace width="0.2em"></mspace> <mi>x</mi> <mo>+</mo> <mi>C</mi> </math> </li><li> <math > <mo>∫</mo> <mo>csc</mo> <mspace width="0.2em"></mspace> <mi>x</mi> <mo>cot</mo> <mspace width="0.2em"></mspace> <mi>x</mi> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mo>csc</mo> <mspace width="0.2em"></mspace> <mi>x</mi> <mo>+</mo> <mi>C</mi> </math> </li></ul>4. Inverse Trigonometric Function<ul><li> <math > <mo>∫</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mi>d</mi> <mi>x</mi> <mo>=</mo> <msup> <mo>tan</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mi>x</mi> <mo>+</mo> <mi>C</mi> </math> </li><li> <math > <mo>∫</mo> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </msqrt> </mfrac> <mi>d</mi> <mi>x</mi> <mo>=</mo> <msup> <mo>sin</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mi>x</mi> <mo>+</mo> <mi>C</mi> </math> </li><li> <math > <mo>∫</mo> <mfrac> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </msqrt> </mfrac> <mi>d</mi> <mi>x</mi> <mo>=</mo> <msup> <mo>cos</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mi>x</mi> <mo>+</mo> <mi>C</mi> </math> </li></ul>

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Where do I find the Integration of a particular function Formula?

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