Find \(\int 5x^4\,dx\).

Find \(\int(6x^2-4x+9)\,dx\).

Find \(\int\left(\frac{3}{x^2}+2\sqrt{x}\right)\,dx\) for \(x>0\).

Find \(\int\left(e^x+\cos x\right)\,dx\).

Find \(\int\left(\sec^2 x+\frac{1}{x}\right)\,dx\) for \(x>0\).

Find \(f(x)\) if \(f'(x)=4x^3-6x\) and \(f(1)=5\).

Find \(y\) if \(\frac{dy}{dx}=3\sqrt{x}\) and \(y=10\) when \(x=4\).

Find \(\int\left(2x^{-3}-7x^{-1}\right)\,dx\) for \(x>0\).

Verify that \(F(x)=\frac{x^5}{5}-2x^2+8\) is an antiderivative of \(f(x)=x^4-4x\).

Find the position function \(s(t)\) if velocity \(v(t)=6t-4\) m/s and \(s(0)=3\) m.