Integrating a trig function produces an additional, unseen variable called the constant C. Leaving this out can instantly make an integration problem wrong even though it is the simplest step. When the derivative of a formula is taken, any constants immediately get eliminated. As a result, when the integral function is performed, the constant returns. However, the actual value of the constant is unknown so you can just write the letter C as a representation.
Doing trig problems requires a keen sense of the different relationships of the functions. Use the mnemonic device, SOH CAH TOA, to remember the base terms Sine, Cosine and Tangent. Use flashcards or other memorization tools to remember the other relationships including:
sin/cos = tan
csc = 1/sin
sec = 1/cos
cot = cos/sin = 1/tan
To perform trig integration problems efficiently, memorize common derivatives. These will be seen constantly in math problem sets and also make up the basic tools to perform any trig integration function. Some common derivatives include:
D(sin x) = cos x
D(cos x) = -sin x
D(tan x) = sec2 x
You may also study the common derivatives for csc, sec and cot.
U substitution is an ingenious trick to perform an integration by substituting a solution with the variable, u. U substitution simply replaces an x in the equation with a u, then takes the derivative of the function. Using the common trig derivatives you have already memorized, identify how the new derivative can be integrated back into a more-workable problem. After you have replaced the derivative, simplify and print the result.