Tom Mattson said:That's exactly the substitution you want to go with. If [itex]u=x-5[/itex] then [itex]x=u+5[/itex], which you can use in the other factor in the integrand.
htoor9 said:So then what? I have integral of (u+10)(u)^(1/3) du.
An integral substitution problem is a type of integration problem in calculus where a change of variables is used to simplify the original integral. This technique is particularly useful for solving integrals that involve complicated functions or expressions.
Integral substitution uses a change of variables to simplify the integral, whereas traditional integration methods such as integration by parts or the power rule involve applying specific rules or formulas to solve the integral.
The steps for solving an integral substitution problem are as follows:
Some common trigonometric substitutions used in integral substitution problems include:
Integral substitution has many applications in real-world problems, particularly in physics and engineering. It can be used to solve problems involving position, velocity, acceleration, and force, as well as in calculating areas, volumes, and probabilities. It is also used in fields such as economics, chemistry, and biology to model and analyze various systems and processes.