Connect with us

Integrals Maths Formulas for Class 12 Chapter 7

Are you looking for Integrals formulas for class 12 Chapter 7? Today, we are going to share Integrals formulas for class 12 Chapter 7 according to student requirements. You are not a single student who is searching Integrals formulas for class 12 chapters 2. According to me, thousands of students are searching Integrals formulas for class 12 Chapter 7 per month. If you have any doubt or issue related to Integrals formulas then you can easily connect with through social media for discussion. Integrals formulas will very helpful to understand the concept and questions of the chapter Integrals.

Formulas – Standard Integrals

  1. \(\int x^ndx=\frac{x^{n+1}}{n+1}+C,n\neq -1\). Particularly, \(\int dx=x+C)\)
  2. \(\int cos\:x\:dx=sin\:x+C\)
  3. \(\int sin\:x\:dx=-cos\:x+C\)
  4. \(\int sec^2x\:dx=tan\:x+C\)
  5. \(\int cosec^2x\:dx=-cot\:x+C\)
  6. \(\int sec\:x\:tan\:x\:dx=sec\:x+C\)
  7. \(\int cosec\:x\:cot\:x\:dx=-cosec\:x+C\)
  8. \(\int \frac{dx}{\sqrt{1-x^2}}=sin^{-1}x+C\)
  9. \(\int \frac{dx}{\sqrt{1-x^2}}=-cos^{-1}x+C\)
  10. \(\int \frac{dx}{1+x^2}=tan^{-1}x+C\)
  11. \(\int \frac{dx}{1+x^2}=-cot^{-1}x+C\)
  12. \(\int e^xdx=e^x+C\)
  13. \(\int a^xdx=\frac{a^x}{log\:a}+C\)
  14. \(\int \frac{dx}{x\sqrt{x^2-1}}=sec^{-1}x+C\)
  15. \(\int \frac{dx}{x\sqrt{x^2-1}}=-cosec^{-1}x+C\)
  16. \(\int \frac{1}{x}\:dx=log\:|x|+C\)

Formulas – Partial Fractions

Partial Fraction Formulas
\(\frac{px+q}{(x-a)(x-b)}\) \(\frac{A}{x-a}+\frac{B}{x-b},a\neq b\)
\(\frac{px+q}{(x-a)^2}\) \(\frac{A}{x-a}+\frac{B}{(x-b)^2}\)
\(\frac{px^2+qx+r}{(x-a)(x-b)(x-c)}\) \(\frac{A}{x-a}+\frac{B}{x-b}+\frac{C}{x-c}\)
\(\frac{px^2+qx+r}{(x-a)^2(x-b)}\) \(\frac{A}{x-a}+\frac{B}{(x-a)^2}+\frac{C}{x-b}\)
\(\frac{px^2+qx+r}{(x-a)(x^2+bx+c)}\) \(\frac{A}{x-a}+\frac{Bx+C}{x^2+bx+c}\)

Formulas – Integration by Substitution

  1. \(\int tan\:x\:dx=log\:|sec\:x|+C\)
  2. \(\int cot\:x\:dx=log\:|sin\:x|+C\)
  3. \(\int sec\:x\:dx=log\:|sec\:x+tan\:x|+C\)
  4. \(\int cosec\:x\:dx=log\:|cosec\:x-cot\:x|+C\)

Formulas – Integrals (Special Functions)

  1. \(\int \frac{dx}{x^2-a^2}=\frac{1}{2a}\:log\:\left |\frac{x-a}{x+a} \right |+C\)
  2. \(\int \frac{dx}{a^2-x^2}=\frac{1}{2a}\:log\:\left |\frac{a+x}{a-x} \right |+C\)
  3. \(\int \frac{dx}{x^2+a^2}=\frac{1}{a}\:tan^{-1}\frac{x}{a}+C\)
  4. \(\int \frac{dx}{\sqrt{x^2-a^2}}=log\:\left |x+\sqrt{x^2-a^2} \right |+C\)
  5. \(\int \frac{dx}{\sqrt{x^2+a^2}}=log\:\left |x+\sqrt{x^2+a^2} \right |+C\)
  6. \(\int \frac{dx}{\sqrt{x^2-a^2}}=sin^{-1}\frac{x}{a}+C\)

Formulas – Integration by Parts

  1. The integral of the product of two functions = first function × integral of the second function – integral of {differential coefficient of the first function × integral of the second function}
    \(\int f_1(x).f_2(x)=f_1(x)\int f_2(x)\:dx-\int \left [ \frac{\mathrm{d} }{\mathrm{d} x}f_1(x).\int f_2(x)\:dx \right ]dx\)
  2. \(\int e^x\left [ f(x)+f'(x) \right ]\:dx=\int e^x\:f(x)\:dx+C\)

Formulas – Special Integrals

  1. \(\int \sqrt{x^2-a^2}\:dx=\frac{x}{2}\sqrt{x^2-a^2}-\frac{a^2}{2}\:log\left | x+\sqrt{x^2-a^2} \right |+C\)
  2. \(\int \sqrt{x^2+a^2}\:dx=\frac{x}{2}\sqrt{x^2+a^2}+\frac{a^2}{2}\:log\left | x+\sqrt{x^2+a^2} \right |+C\)
  3. \(\int \sqrt{a^2-x^2}\:dx=\frac{x}{2}\sqrt{a^2-x^2}+\frac{a}{2}\:sin^{-1}\frac{x}{a}+C\)
  4. \(ax^2+bx+c=a\left [ x^2+\frac{b}{a}x+\frac{c}{a} \right ]=a\left [ \left ( x+\frac{b}{2a} \right )^2+\left ( \frac{c}{a}-\frac{b^2}{4a^2} \right ) \right ]\)

Summary of Integrals formulas

We have listed top important formulas for Integrals for class 12 Chapter 7 which helps support to solve questions related to chapter Integrals. I would like to say that after remembering the Integrals formulas you can start the questions and answers solution of the Integrals chapter. If you faced any problem to find the solution of Integrals questions, please let me know through commenting or mail.

Maths Formulas for Class 12 by Chapters

Here Check Maths formulas for class 12 by chapter wise.

Continue Reading
Advertisement