Indefinite Integral Formula

Basics of Indefinite Integral Formula

Indefinite Integral Formula ahs been made from the reverse operations of differentiation or anti-differentiation.
\( \begin{aligned} \displaystyle
\frac{d}{dx}x^3 &= 3x^2 &\Rightarrow \int{3x^2}dx &= x^3 \\
\frac{d}{dx}(x^3 + 4) &= 3x^2 &\Rightarrow \int{3x^2}dx &= x^3 + 4 \\
\frac{d}{dx}(x^3 -2) &= 3x^2 &\Rightarrow \int{3x^2}dx &= x^3 – 2 \\
\end{aligned} \\ \)
The general formula of indefinite integral is;
$$\int{x^n}dx = \frac{x^{n+1}}{n+1} + C $$

Practice Questions

Question 1

Find \( \displaystyle \int{4}dx \).

Question 2

Find \( \displaystyle \int{2x}dx \).

Question 3

Find \( \displaystyle \int{\frac{4x^3}{3}}dx \).

Question 4

Find \( \displaystyle \int{(3x^2 + 2x + 4)}dx \).

Question 5

Find \( \displaystyle \int{\frac{3}{2x^2}}dx \).

Question 6

Find \( \displaystyle \int{\frac{6x^3+2x^2-3x}{x}}dx \).

Question 7

Find \( \displaystyle \int{x(x-2)}dx \).