Original
Compute:
{{MATH_317}}
{{CMD_318}}
We try to guess the antiderivative. Start with a guess of
{{MATH_319}}
Take the derivative of your guess to see if it is correct:
{{MATH_320}}
Ah! So we need only multiply our original guess by {{MATH_321}}. We now
find
{{MATH_322}}
{{CMD_323}}
{{CMD_324}}
{{CMD_325}}
Compute:
{{MATH_326}}
{{CMD_327}}
We notice that the numerator is the derivative of the denominator, i.e., the function that we are integrating has the form {{MATH_328}}.
{{MATH_329}}
Take the derivative of your guess to see if it is correct:
{{MATH_330}}
Therefore,
{{MATH_331}}
{{CMD_332}}
{{CMD_333}}
{{CMD_334}}
Compute:
{{MATH_335}}
{{CMD_336}}
We'll start with a guess of
{{MATH_337}}
Take the derivative of your guess to see if it is correct:
{{MATH_338}}
We are only off by a factor of {{MATH_339}}, so we need to multiply our
original guess by this constant to get the solution,
{{MATH_340}}
{{CMD_341}}
{{CMD_342}}