Question

College Calculus - hyperbolic functions (see attachment)

Answer 1

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

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
`\int\limits^x_4 {g(t)} \, dt = g(x)`

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))))