Say we are solving an indefinite integral ∫x√(2x+1) dx.(adsbygoogle = window.adsbygoogle || []).push({});

According to the textbook, the solution goes like this.

Let u = 2x+1. Then x = (u-1)/2.

Since √(2x+1) dx = (1/2)√u du,

x√(2x+1) dx = [(u-1)/2] * (1/2)√u du.

∫x√(2x+1) dx = ∫[(u-1)/2] * (1/2)√u du. <= What justifies this??

The rest is just trivial calculation.

The only theorem I could rely on here to solve this problem was,

-------------------------------------------------------------------

If u=g(x) is a differentiable function whose range is an interval I, and f is continuous no I, then

∫f(g(x))g'(x) dx = ∫f(u) du.

--------------------------------------------------------------------

Which is so called the substitution rule.

How can this theorem justify the process of the solution I wrote above?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Substitution Method on indefinite integral

Loading...

Similar Threads for Substitution Method indefinite |
---|

B Methods of integration: direct and indirect substitution |

A Integral equations -- Picard method of succesive approximation |

I Partial derivatives method |

I Derivative When Substituting Variables |

B Not following an integral solution |

**Physics Forums | Science Articles, Homework Help, Discussion**