Question

Evaluate the following integral. $$ \int \frac{dx}{\sqrt{x^2 + 2x + 101}} $$ $$ \int \frac{dx}{\sqrt{x^2 + 2x + 101}} = \boxed{} $$ (Type an exact answer.)

Name: evaluate the following integral int fracdxsqrtx2 2x 101 int fracdxsqrtx2 2x 101 boxed type an exact answer 89704
Uploaded: 2022-03-25T16:35:18-08:00
Duration: 1 min 35 s
Channel: Nick Johnson
Description: evaluate the following integral int fracdxsqrtx2 2x 101 int fracdxsqrtx2 2x 101 boxed type an exact answer 89704

          Evaluate the following integral.
$$ \int \frac{dx}{\sqrt{x^2 + 2x + 101}} $$
$$ \int \frac{dx}{\sqrt{x^2 + 2x + 101}} = \boxed{} $$
(Type an exact answer.)

$evaluate the following integral int fracdxsqrtx2 2x 101 int fracdxsqrtx2 2x 101 boxed type an exact answer 89704$

Added by Christina S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Nick Johnson

03/25/2022

Step 1

The quadratic expression in the denominator is $x^2 + 2x + 101$. To complete the square for $x^2 + 2x$, we take half of the coefficient of $x$ (which is $2/2 = 1$) and square it ($1^2 = 1$). So, we can write $x^2 + 2x + 101$ as: $$ x^2 + 2x + 101 = (x^2 + 2x + 1) Show more…

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Evaluate the following integral. $$ \int \frac{dx}{\sqrt{x^2 + 2x + 101}} $$ $$ \int \frac{dx}{\sqrt{x^2 + 2x + 101}} = \boxed{} $$ (Type an exact answer.)