Evaluate the integral.

Question

∫ dt / sqrt (t^2 - 8t + 25).?

Answer 1

To find ,

Apply formula : .

First write the expression :  , into a perfect square trinomial.

To change the expression into a perfect square trinomial add (half the t coefficient)² to each side of the expression

 Here t coefficient = - 8. so, (half the t coefficient)² = (- 8/2)²= 16

Add and subtract16 to the expression.

t ² - 8t + 16 + 25 - 16

(t - 4)² + 9

(t - 4)² + 3².

⇒

.