Integrals of Other Trig Functions: Videos & Practice Problems

Which of the following gives the correct antiderivative of tan x for x in an interval where cos x ≠ 0?

Which antiderivative is correct for cot x (where sin x ≠ 0)?

Use the standard trick to compute ∫ sec x dx.

Compute ∫ csc x dx by applying the analogous conjugate trick to the secant case.

Evaluate ∫ sec^4 x tan x dx by choosing an appropriate substitution that uses the derivative of sec x.

Evaluate the definite integral ∫_{π/6}^{π/3} sec x dx. Be careful with the logarithmic antiderivative and compute an exact value.

Does the improper integral ∫_{0}^{π/2} tan x dx converge?

Evaluate ∫ tan^3 x sec^2 x dx using an appropriate substitution.

Compute ∫ cos^4 x dx using power-reduction identities.

Find ∫ csc^3 x dx using a substitution that separates factors and uses u = cot x (or the standard reduction approach).

What is the simplest correct strategy to integrate the function (tan^2 x)/(sec x)?

Evaluate ∫ (sec x tan x)/(1 + tan^2 x) dx by simplifying the integrand first.

Which derivative identity justifies that d/dx [ln|sec x + tan x|] = sec x?

Compute ∫ sec^5 x dx using the reduction formula or integration by parts to reduce the power to known integrals.

Compute ∫ sin^4 x dx using power-reduction identities and present the antiderivative in terms of sines of multiple angles.

Evaluate the definite integral ∫_{π/4}^{π/3} tan x dx and provide the exact value.

Which statement about the antiderivative F(x) = ln|sec x + tan x| is true regarding its domain and the absolute value?

Evaluate ∫ (tan^2 x)/(1 + tan^2 x) dx and give the antiderivative in simplest form.

Which of the following is an antiderivative of csc x cot x?

Compute ∫ tan^2 x sec^4 x dx by choosing u = tan x and expanding appropriately.

Which strategy is best to integrate (tan^2 x)/(sec x + 1)? Choose the most direct algebraic approach.

Compute the integral I = ∫_{0}^{π/2} sin^2 x dx.

Evaluate ∫ (sec x tan x)/(1 + sec x) dx by choosing an appropriate substitution.