Calculus Examples

$e^{5 \ln (x + \cos (x))}$

Step 1

Simplify $5 \ln (x + \cos (x))$ by moving $5$ inside the logarithm.

$e^{\ln ({(x + \cos (x))}^{5})}$

Step 2

Exponentiation and log are inverse functions.

${(x + \cos (x))}^{5}$

Step 3

Use the Binomial Theorem.

$x^{5} + 5 x^{4} \cos (x) + 10 x^{3} \cos^{2} (x) + 10 x^{2} \cos^{3} (x) + 5 x \cos^{4} (x) + \cos^{5} (x)$