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Each term is integrated according to the formula:

ax^b --> (a/(b+1))x^(b+1)

A constant k integrates to kx 

Since this is indefinite inte...

Each term is differentiated according to the formula:

y = ax^b --> dy/dx = b*ax^(b-1)

Constants differentiate to zero.

Therefore in this...

Remember that the gradient of a curve is expressed as dy/dx. This can be solved by using the chain rule:

dy/dx = dy/dt*dt/dx. The dt in the denominator of the first term, and the numerato...

Rearranging the terms of the series into the usual "descending order" for polynomials, we get a series expansion of:  

ax^{n-1 +}........ax + a

A basic pro...