College Calculus - hyperbolic functions (see attachment)

g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))

Step-by-step explanation:

Using the fundamental theorem of calculus

Taking the derivative of the integral gives back the function

Since the lower limit is a constant when we take the derivative it is zero

d/dx

g(t) = sinh^-1 ( ln(7t^6 +3) / sqrt( 8+cot( t^( 3+t))))

Replacing t with x

g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))

step-by-step explanation: