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### Section 5-1 : Indefinite Integrals

1. Evaluate each of the following indefinite integrals.
1. $$\displaystyle \int{{10{x^9} - 12{x^3} - 5\,dx}}$$
2. $$\displaystyle \int{{10{x^9} - 12{x^3}\,dx - 5}}$$
2. Evaluate each of the following indefinite integrals.
1. $$\displaystyle \int{{{t^7} + 33{t^2} + 8t\,dt}}$$
2. $$\displaystyle \int{{{t^7}\,dt}} + 33{t^2} + 8t$$
3. Evaluate each of the following indefinite integrals.
1. $$\displaystyle \int{{6{x^5} - 7{x^3} + 12{x^2} - 10\,dx}}$$
2. $$\displaystyle \int{{6{x^5} - 7{x^3}\,dx}} + 12{x^2} - 10$$
3. $$\displaystyle \int{{6{x^5}\,dx}} - 7{x^3} + 12{x^2} - 10$$
4. Evaluate each of the following indefinite integrals.
1. $$\displaystyle \int{{21{x^6} - 9{x^5} - {x^3} - x\,dx}}$$
2. $$\displaystyle \int{{21{x^6} - 9{x^5} - {x^3}\,dx}} - x$$
3. $$\displaystyle \int{{21{x^6} - 9{x^5}\,dx}} - {x^3} - x$$

For problems 5 – 9 evaluate the indefinite integral.

1. $$\displaystyle \int{{8{t^5} - 15{t^2} - 1\,dt}}$$
2. $$\displaystyle \int{{120{y^9} - 24{y^5} - 4{y^3}\,dy}}$$
3. $$\displaystyle \int{{dw}}$$
4. $$\displaystyle \int{{{x^9} + 14{x^6} - 10{x^3} + 13x\,dx}}$$
5. $$\displaystyle \int{{8{x^6} - {x^4} - 7{x^2} + 11x - 12\,dx}}$$
6. Determine $$f\left( x \right)$$ given that $$f'\left( x \right) = 16{x^4} - 9{x^2} - x$$.
7. Determine $$g\left( t \right)$$ given that $$g'\left( t \right) = 4{t^5} + 16{t^2} - 18t + 72$$.
8. Determine $$R\left( z \right)$$ given that $$R'\left( z \right) = 4{z^{15}} + 121{z^{10}} + 20{z^5} + z - 4$$.
9. Determine $$f\left( x \right)$$ given that $$f''\left( x \right) = 8{x^3} - 12x + 3$$.