Basic indefinite integration

Find \(\int \left(x - \frac{3}{x^2}\right) dx\). [3]

Find \(\int (20x^4 + 6x^{-\frac{2}{3}}) dx\). [4]

Find \(\int (12x^5 + \sqrt[5]{x} + 7) dx\). [5]

Find \(\int \left(x^{\frac{1}{2}} + \frac{6}{x^3}\right) dx\). [5]

Find \(\int \left(x^4 + \frac{1}{x^3}\right) dx\). [4]

Given that \(\frac{dy}{dx} = \frac{1}{6x^2}\), find \(y\). Circle your answer. \(\frac{-1}{3x^3} + c\) \quad \(\frac{1}{2x^3} + c\) \quad \(\frac{-1}{6x} + c\) \quad \(\frac{-1}{3x} + c\) [1 mark]

Find $$\int \left(x^2 + x^{\frac{1}{2}}\right) dx$$ [2 marks]

Find $$\int(\frac{1}{2}x^2 - 9\sqrt{x} + 4) dx$$ giving your answer in its simplest form.

Find \(\int\left(5x^4 + 3x^{-2} - 2\right)dx\). [3]

Find $$\int (x^4 - 6x^2 + 7) dx$$ giving your answer in simplest form. [3]

Find $$\int (x^4 - 6x^2 + 7) dx$$ giving your answer in simplest form. [3]