question\ncalculate the integral and write the answer in simplest form.\n int (4 - 3x^{3}-5x^{-2})dx

Explanation:

Step1: Apply integral sum - difference rule

$\int (4 - 3x^{3}-5x^{-2})dx=\int 4dx-\int 3x^{3}dx-\int 5x^{-2}dx$

Step2: Apply constant - multiple rule

$=\ 4\int dx-3\int x^{3}dx - 5\int x^{-2}dx$

Step3: Use power rule for integration $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C(n\neq - 1)$ and $\int dx=x + C$

$4x-3\times\frac{x^{3 + 1}}{3+1}-5\times\frac{x^{-2 + 1}}{-2+1}+C$

Step4: Simplify the expression

$4x-\frac{3}{4}x^{4}+5x^{-1}+C$ $4x-\frac{3}{4}x^{4}+\frac{5}{x}+C$

Answer:

$4x-\frac{3}{4}x^{4}+\frac{5}{x}+C$