Why is it necessary to include a constant 'c' when finding an antiderivative?

Find an antiderivative for the function $5x^2-x+7$.

Find an antiderivative of ${\sec }^2(5x-1)$.

What is the term used for the function inside an indefinite integral?

Evaluate the integral.

$\int t^2(4t^3-2{)}^{3}dt$

What is the integral of sin(x) with respect to x?

Evaluate the integral.

$\int \cos x\cos \left(\sin x\right)dx$

Evaluate the integral.

$\int x\cos x^2{\sin }^6{x}^{2}dx$

Why is an initial condition necessary when solving a differential equation?

Integrate the function f(x) = 4x^3 - 6x + 2 using the power rule.

Find the solution to the initial value problem: $(t+4)\frac{dz}{dt}=z^2+9$ for $t>-4$, $z\left(0\right)=0$.