# Integration

## Problem 5: Integral of (6z - 1) dz / sqrt[ (2z + 1)^3 ] by Algebraic Substitution

**Problem**

Evaluate $\displaystyle \int \dfrac{(6z - 1) \, dz}{\sqrt{(2z + 1)^3}}$

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## Problem 4: Integral of (y dy) / 4th root(1 + 2y) by Algebraic Substitution

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## Problem 3: Integral of (x^3 dx) / (x^2 + 1)^3 by Algebraic Substitution

**Problem**

Evaluate $\displaystyle \int \dfrac{x^3 \, dx}{(x^2 + 1)^3}$

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## Problem 2: Integral of y^3 * sqrt(2y^2 + 1)dy by Algebraic Substitution

**Problem**

Evaluate $\displaystyle \int y^3\sqrt{2y^2 + 1} \,\, dy$

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**Problem**

Evaluate $\displaystyle \int_0^1 \dfrac{x \, dx}{x^2 + 2}$.

A. 0.2027 | C. 0.2270 |

B. 0.2207 | D. 0.2072 |

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**Problem**

Evaluate $\displaystyle \int_0^9 \dfrac{1}{\sqrt{1 + \sqrt{x}}}$

A. 4.667 | C. 5.333 |

B. 3.227 | D. 6.333 |

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## Perimeter of the curve r = 4(1 + sin theta) by integration

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## Example 03 | The General Power Formula

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## Example 02 | The General Power Formula

**Problem**

Evaluate $\displaystyle \int \sqrt{ax + b} ~ dx$.

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## Example 01 | The General Power Formula

**Problem**

Evaluate $\displaystyle \int \left( \sqrt{x} + x\sqrt{x} + \dfrac{1}{\sqrt{x}} \right) \, dx$

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