Questions from General Calculus

Q: Write out the form of the partial fraction decomposition of the function

Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients.

Q: Evaluate the integral. f x3/x3 + 1,

Evaluate the integral. f x3/x3 + 1, dx

Q: Evaluate the integral. f dx/x (x2 +

Evaluate the integral. f dx/x (x2 + 4)2

Q: (a). If is a complex-valued function of a

(a). If is a complex-valued function of a real variable, its indefinite integral f u (x) dx is an antiderivative of u. Evaluate (b). By considering the real and imaginary parts of the integral in pa...

Q: Evaluate the integral. f x4 + 3x2 + 1/

Evaluate the integral. f x4 + 3x2 + 1/x5 + 5x3 + 5x, dx

Q: Evaluate the integral. f x – 3/ (x2

Evaluate the integral. f x – 3/ (x2 + 2x + 4)2, dx

Q: Evaluate the integral. f 3x2 + x + 4/

Evaluate the integral. f 3x2 + x + 4/ x4 + 3x2 + 2, dx

Q: Make a substitution to express the integrand as a rational function and

Make a substitution to express the integrand as a rational function and then evaluate the integral.

Q: Make a substitution to express the integrand as a rational function and

Make a substitution to express the integrand as a rational function and then evaluate the integral.

Q: Make a substitution to express the integrand as a rational function and

Make a substitution to express the integrand as a rational function and then evaluate the integral.