Question

1. evaluate the indefinite integral: $int(\frac{7x^{4}}{5}-\frac{x^{5}}{3})dx=\frac{7x^{5}}{25}-\frac{x^{6}}{18}+c$.

Explanation:

Step1: Apply integral rules

Use $\int(x^n)dx=\frac{x^{n + 1}}{n+1}+C$ ($n
eq - 1$) and $\int kdx=kx + C$ (k is a constant).
For $\int(7x^4-5x^5 - 3)dx=\int7x^4dx-\int5x^5dx-\int3dx$.

Step2: Integrate each term

$\int7x^4dx=7\times\frac{x^{4 + 1}}{4+1}=\frac{7x^5}{5}$, $\int5x^5dx=5\times\frac{x^{5+1}}{5 + 1}=\frac{5x^6}{6}$, $\int3dx=3x$.

Step3: Combine results

$\int(7x^4-5x^5 - 3)dx=\frac{7x^5}{5}-\frac{5x^6}{6}-3x + C$.

Answer:

$\frac{7x^5}{5}-\frac{5x^6}{6}-3x + C$