Find an antiderivative for the function $4x^3$.

Find all the antiderivatives of the function $f\left(x\right)=-5\sin x+2$.

Determine whether the following statement is true or false:

The antiderivative of $(5x+2{)}^{-2}$ is $-\frac{1}{5}(5x+2{)}^{-1}+C$.

Determine the following indefinite integral:

$\int e^{7x}dx$

Evaluate the indefinite integral: $\int ({\sec }^{2}x+4x^2-5x)dx$

Evaluate the indefinite integral: $\int \frac{6}{x\sqrt{x^2-4}}dx$