Use substitution and partial fractions to find the indefinite integral

Take the constant out,

Now let's apply integral substitution:

Now to use partial fractions, denominator of the integrand needs to be factored,

Let's split the middle term,

Now let's write it as sum of partial fractions:

Multiply the above by the LCD,

Equating the coefficients of the like terms,

   -----------------------------(1)

  ----------------------------(2)

Solve the above linear equations to get the values of A...

Take the constant out,

Now let's apply integral substitution:

Now to use partial fractions, denominator of the integrand needs to be factored,

Let's split the middle term,

Now let's write it as sum of partial fractions:

Multiply the above by the LCD,

Equating the coefficients of the like terms,

   -----------------------------(1)

  ----------------------------(2)

Solve the above linear equations to get the values of A and B,

Add equation 1 and 2,

Plug the value of A in equation 1,

Plug in the values of A and B in the partial fraction template,

Take the constant out,

Apply the sum rule,

Now use the common integral:

Substitute back 

Simplify and add a constant C to the solution,