Please help!!!!

Problem 1. (1 point) Find the antiderivative F of f(x) = 4 - 3(1 + x2)" that satisfies F(1) = -3. F(x) =Problem 2. (1 point) Find the function f (x) described by the given initial value problem. f\"(X) = ZSin, for) = 0, \") =0 f(x) = Problem 3. (1 point) Using an upper-case "C" for any arbitrary constants, find the general indefinite integral [(-5x28+x2:1)dx Integral = Problem 4. (1 point) Use the Fundamental Theorem of Calculus to find the derivative of 12 F(x) = tan(t5)dt F'(x) = [NOTE: Enter a function as your answer] Problem 5. (1 point) Use the Fundamental Theorem of Calculus to find the derivative of dy dx [NOTE: Enter a function as your answer. Make sure that your syntax is correct, i.e. remember to put all the necessary (, ), etc. ] Problem 6. (1 point) Evaluate the definite integral Problem 7. (1 point) Evaluate the integral 7 22 fx+6d 2 1/3? x Problem 8. (1 point) Evaluate the integral / (3ex + 7 cos x) dx. Answer: Problem 9. (1 point) Logarithms as anti-derivatives. -6 dx = x(In x)2 Hint: Use the natural log function and substitution.Problem 10. (1 point) Evaluate 1: /3 tan x dx. Answer: Problem 11. (1 point) Evaluate the indefinite integral. 4e * sin(ex ) dx =Problem 12. (1 point) Find the the general antiden'vative F(x) of the function f (x) given below. Note that you can check your answer by differentiation. f(x) = 3x sin(x2) antiderivative F(x) =