Q. 17 - Calculus

Question

Indefinite integrals: Use integration formulas, algebra, and

educated guess-and-check strategies to find the following

integrals .

$\int \left(3x^4-x^3+2\right)dx$

Step-by-Step Solution

Answer

The integral is $\left(\frac{3x^5}{5}-\frac{x^4}{4}+2x+C\right)$ .

Step 1. Given information .

Consider the given integral $\int \left(3x^4-x^3+2\right)dx$.

Step 2. Using the sum rule .

The sum rule is $\int f\left(x\right)\pm g\left(x\right) dx=\int f\left(x\right) dx\pm \int g\left(x\right) dx$.

Step 3. Find the integral .

$$\begin{gathered} \Rightarrow \int \left(3x^4-x^3+2\right) dx \\ \Rightarrow \int 3x^4 dx-\int x^3 dx+\int 2 dx \\ \Rightarrow \frac{3x^5}{5}-\frac{x^4}{4}+2x+C \end{gathered}$$