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Starting with ∫a^x dx ,
We can re-write a^x using logs as e^ln(a)*x using some of their properties
We use the substitution u = ln(a)*x (as such du/dx = ln(a)) all...

You start by seperating the variables giving,

(1/x)*dx=(-6)*dt

you then integrate both sides with respect to the variables,

ln(x)=-6*t+c

you then subsitute in the given conditi...

x^3/3  +  1/x

Binomial:

1. A single trial has only 2 possible outcomes: success or failure

2. A fixed number of trials, n

3. Trials are independent

...

In order to integrate (cosx)^3, there is no given rule (by-parts, 'try' method, chain rule) which we can follow. We would need to split it into (cosx)^2 and cosx. Then use the identity: (sinx)^2 + (cosx)^...