১ম অনুচ্ছেদ
    1. \(\int \{f(x) \pm \varphi(x)\} dx = \int f(x) dx \pm \int \varphi(x) dx\)
    2. \(\int cf(x) dx = c \int f(x) dx\)

  2. কিছু প্রমিত ফাংশনের যোগজ:

    1. \(\int x^n dx = \frac{x^{n+1}}{n+1} + c\) যখন \(n \neq -1\)
    2. \(\int \frac{1}{x} dx = \ln|x| + c\)
    3. \(\int \frac{f'(x)}{f(x)} dx = \ln|f(x)| + c\)
    4. \(\int \sin x \, dx = -\cos x + c\)
    5. \(\int \cos x \, dx = \sin x + c\)
    6. \(\int \sec^2 x \, dx = \tan x + c\)
    7. \(\int \text{cosec}^2 x \, dx = -\cot x + c\)
    8. \(\int e^{mx} dx = \frac{1}{m} e^{mx} + c\)
    9. \(\int a^x dx = \frac{a^x}{\ln a} + c\)
    10. \(\int \text{cosec } x \cot x \, dx = -\text{cosec } x + c\)
    11. \(\int \sec x \tan x \, dx = \sec x + c\)
    12. \(\int \frac{dx}{\sqrt{1 - x^2}} = \sin^{-1} x + c\)
    13. \(\int -\frac{dx}{\sqrt{1 - x^2}} = \cos^{-1} x + c\)
    14. \(\int \frac{dx}{1 + x^2} = \tan^{-1} x + c\)
    15. \(\int -\frac{dx}{1 + x^2} = \cot^{-1} x + c\)
    16. \(\int \frac{dx}{x\sqrt{x^2 - 1}} = \sec^{-1} x + c\)
    17. \(\int -\frac{dx}{x\sqrt{x^2 - 1}} = \text{cosec}^{-1} x + c\)
    18. \(\int \frac{1}{2\sqrt{x}} dx = \sqrt{x} + c\)
২য় অনুচ্ছেদ

  1. \(\int \cot x \, dx = \ln|\sin x| + c\)

  2. \(\int \sec x \, dx = \ln|\sec x + \tan x| + c = \ln\left|\tan\left(\frac{\pi}{4} + \frac{x}{2}\right)\right| + c\)

  3. \(\int \text{cosec } x \, dx = \ln\left|\tan\frac{x}{2}\right| + c = -\ln|\text{cosec } x + \cot x| + c\)

  4. \(\int \frac{f'(x)}{f(x)} dx = \ln|f(x)| + c\)

৩য় অনুচ্ছেদ

    1. \(\int \frac{dx}{x^2 - a^2} = \frac{1}{2a} \ln \left| \frac{x - a}{x + a} \right| + c;\)

    2. \(\int \frac{dx}{\sqrt{a^2 - x^2}} = \sin^{-1}\frac{x}{a} + c\)

    3. \(\int \frac{dx}{\sqrt{x^2 - a^2}} = \ln \left| x + \sqrt{x^2 - a^2} \right| + c\)

    4. \(\int \frac{dx}{\sqrt{x^2 + a^2}} = \ln \left| x + \sqrt{x^2 + a^2} \right| + c\)

    5. \(\int \sqrt{a^2 - x^2} = \dfrac{x \sqrt{a^2 - x^2}}{2} + \dfrac{a^2}{3} sin^{-1}\frac{x}{a} + c\)

৪র্থ অনুচ্ছেদ

  1. মূলদীয় ফাংশনকে আংশিক ভগ্নাংশে বিভক্ত করার কৌশল

    1. \(\dfrac{ax^2 + bx + c}{(x - l)(x - m)(x - n)}\) আকৃতি হলে \(\dfrac{ax^2 + bx + c}{(x - l)(x - m)(x - n)} = \dfrac{A}{x - l} + \dfrac{B}{x - m} + \dfrac{C}{x - n}\)
    2. \(\dfrac{ax^2 + bx + c}{(x - l)^2(x - m)}\) আকৃতি হলে \(\dfrac{ax^2 + bx + c}{(x - l)^2(x - m)} = \dfrac{A}{x - l} + \dfrac{B}{(x - l)^2} + \dfrac{C}{x - m}\)
    3. \(\dfrac{ax^2 + bx + c}{(x^2 + l)(x + m)}\) আকৃতি হলে \(\dfrac{ax^2 + bx + c}{(x^2 + l)(x + m)} = \dfrac{Ax + B}{x^2 + l} + \dfrac{C}{x + m}\)
    4. \(\dfrac{Ax^2 + bx + c}{(x - l)(x - m)}\) আকৃতি হলে \(\dfrac{Ax^2 + bx + c}{(x - l)(x - m)} = A + \dfrac{B}{x - l} + \dfrac{C}{x - m}\)
    5. \(\dfrac{Ax^3 + bx^2 + cx + d}{(x - l)^2}\) আকৃতি হলে \(\dfrac{Ax^3 + bx^2 + cx + d}{(x - l)^2} = Ax + B + \dfrac{C}{x - l} + \dfrac{D}{(x - l)^2}\)
৫ম অনুচ্ছেদ

  1. \(\int uv \, dx = u \int v \, dx - \int \left\{ \frac{d}{dx}(u) \int v \, dx \right\} dx\)

  2. \(\int e^x \{f(x) + f'(x)\} \, dx = e^x f(x) + c\)

৬ষ্ঠ অনুচ্ছেদ

  1. \(\int_a^b f(x) \, dx = \int_a^b f(t) \, dt\). যেমন : \(\int_0^1 x^2 \, dx = \int_0^1 t^2 \, dt\)

  2. \(\int_a^b f(x) \, dx = -\int_b^a f(x) \, dx\)

  3. \(\int_0^a f(x) \, dx = \int_0^a f(a - x) \, dx\)

৭ম অনুচ্ছেদ

  1. \(x = a, x = b, y = f(x)\) এবং \(x\)-অক্ষ দ্বারা আবদ্ধ সমতল ক্ষেত্রের ক্ষেত্রফল, \(A = \int_a^b y \, dx\)

    কিন্তু \(x = f(y)\) এবং \(y\)-অক্ষ দ্বারা আবদ্ধ সমতল ক্ষেত্রের ক্ষেত্রফল, \(A' = \int_a^b x \, dy\)

  2. \(y_1 = f_1(x), y_2 = f_2(x)\) বক্ররেখাদ্বয় এবং \(x = a\) ও \(x = b\) দ্বারা আবদ্ধ ক্ষেত্রের ক্ষেত্রফল \(\int_a^b (y_1 - y_2) \, dx\)