Question

Integration of x².a^x

Answer 1

Answer:

In this tutorial we shall find the integral of 1 over x^2-a^2.

The integration is of the form

∫1x2–a2dx=12aln(x–ax+a)+c

Now we have an integral to evaluate,

I=∫1x2–a2dx⇒I=∫1(x–a)(x+a)dx⇒I=12a∫[(x+a)–(x–a)](x–a)(x+a)dx⇒∫dxx2–a2=12a[∫1x–adx–∫1x+adx]

Using the integral formula ∫f′(x)f(x)dx=lnf(x)+c, we have

∫dxx2–a2=12a[ln(x–a)–ln(x+a)]+c⇒∫dxx2–a2=12alnx–ax+a+c

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