Say we're asked to find the following integrals: \[\int \begin{pmatrix} x^2 - 1 \end{pmatrix} \sqrt{x+2}.dx, \quad \int 3x \sqrt[4]{4x - 5} dx\] where, in each case, the integrand is a product of two functions:
To find integrals, like those shown above, we use the method of substitution by making a change of variable, \(u\), using either of the following two options:
Say we have to find the integral \(\int \begin{pmatrix}x^2 + 1 \end{pmatrix} \sqrt{2x-1}. dx\), then we could use either of the following two substitutions:
In the following tutorial we show how to find the integral \(\int \begin{pmatrix}x^2 + 1 \end{pmatrix} \sqrt{2x-1}. dx\), using the change of variable \(u = 2x - 1\).
In the following tutorial we show how to find the integral \(\int \begin{pmatrix}x^2 + 1 \end{pmatrix} \sqrt{2x-1}. dx\), using the change of variable \(u = \sqrt{2x-1}\).
Using the substitution of your choice, find each of the following integrals:
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