Evaluate : intsin3"x"sin5"x\ dx"

A function `phi(x)` is called a primitive of `f(x)`; if `phi'(x) = f(x)`

Some important formulas of integration

Examples of integration: (i) `x^4` (ii) `3^x`

Theorem: `d/dx(int f(x) dx) = f(x)`

The integral of the product of a constant and a function = the constant x integral of function

`int {f(x) pm g(x)} dx = int f(x) dx pm int g(x) dx`

Geometrical interpretation of indefinite integral

Comparison between differentiation and integration

By substitution: Theorem: If `int f(x) dx = phi(x)` then `int f(ax+b) dx = 1/a phi(ax + b)dx`

Examples: `1/ (cos3x+1) dx` and `1/((sqrt (x+a) + sqrt (x+b))) dx`