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### Section 5.1 : Indefinite Integrals

1. Evaluate each of the following indefinite integrals.
1. $$\displaystyle \int{{6{x^5} - 18{x^2} + 7\,dx}}$$
2. $$\displaystyle \int{{6{x^5}\,dx}} - 18{x^2} + 7$$
Solution
2. Evaluate each of the following indefinite integrals.
1. $$\displaystyle \int{{40{x^3} + 12{x^2} - 9x + 14\,dx}}$$
2. $$\displaystyle \int{{40{x^3} + 12{x^2} - 9x\,dx}} + 14$$
3. $$\displaystyle \int{{40{x^3} + 12{x^2}\,dx}} - 9x + 14$$
Solution

For problems 3 – 5 evaluate the indefinite integral.

1. $$\displaystyle \int{{12{t^7} - {t^2} - t + 3\,dt}}$$ Solution
2. $$\displaystyle \int{{10{w^4} + 9{w^3} + 7w\,\,dw}}$$ Solution
3. $$\displaystyle \int{{{z^6} + 4{z^4} - {z^2}\,dz}}$$ Solution
4. Determine $$f\left( x \right)$$ given that $$f'\left( x \right) = 6{x^8} - 20{x^4} + {x^2} + 9$$. Solution
5. Determine $$h\left( t \right)$$ given that $$h'\left( t \right) = {t^4} - {t^3} + {t^2} + t - 1$$. Solution