Find the most general antiderivative of the function.

Question

1. g(t) = (1+ 3sqrt(t)−5t^2)/( tsqrt(t)) .

2. h(u) = ( u − ((3)/( cubed sqrt(u)))^2  

3. r(θ) = (sec θ − tan θ)^2 .

Answer 1

Step 1:

(1)

The function is .

The anti derivative of the function means integration.

.

Apply integrate on each side with respect to .

Solution :

(1) .

Answer 2

Step 1:

(2)

The function is .

The anti derivative of the function means integration.

Simplify the function .

Integrate on each side with respect to .

Solution :

(2) .

Answer 3

Step 3:

(3)

The function is .

The anti derivative of the function means integration.

Simplify the function .

Integrate on each side with respect to .

Solution :

(3) .