in this video I'm going to give you a list of integration formulas for common trig functions so let's begin the indefinite integral of sin x is cine X and you don't want to forget plus C and the indefinite integral of cosine X DX is going to be positive sinx plus C now sometimes you might see these trig functions in this format the indefinite integral of sin x I mean of sin ax + B it's going to be negative cosine the angle ax plus b will be the same but then it's divided by the derivative of ax plus b which is a plus c now it works the same way for cosine so the indefinite integral of cosine ax + b you could write it this way instead of just putting over a you could write 1/ a s a x + B plus C now this also works for the other trig functions like secant cosecant tangent cotangent if you have a linear function on the inside you just have to divide your answer by a and this is ax to the first Power Plus B now the indefinite integral of tangent X it's the natural log of secant x plus C now secant is the reciprocal of cosine secant x is 1/ cosine so this is Ln cine x + C if you move the ne 1 to the front you get cosine x^ 1 which is 1 / cosine which is secant so that's why we have the negative sign there now the anti-derivative or the indefinite integral of coent x DX is going to be the natural log of sinx + C alternatively you could set it equal to the natural log of negative natural log of cosecant X plus C so that's the indefinite integral for tangent and coent now the indefinite integral of secant x DX is going to be the natural log secant X+ tangent x + C the indefinite integral for cosecant X is very similar we're going to have a natural log function but instead of secant it's going to be cosecant and instead of plus we have minus instead of tangent we have cotangent now the indefinite integral of not s but sin^2 X this is going to be 12 x -4 sin 2x now for those of you who don't remember the double angle formulas sin 2x is 2 sinx cosine X I'm going to put the trig formula sheet in the description section below for those of you who need to review the trig formulas so we can write this as 12 x - sin x cine X that's another way to represent the answer and the indefinite integral of cine 2 x DX is very similar 12 x but instead of minus it's going to be 12x +/ 14x sin 2x+ C very similar to sin squ the only difference is instead of a minus you have a plus so we can also write it as 12 X+ sin x cine X plus C by the way if you want a list of these integration formulas feel free to check out the formula sheet below I have two formula sheets the trig formula sheet and the integration formulas uh that sheet sheet as well so feel free to download both of them if you want this cuz there's a lot of other integration formulas out there that you'll find useful for those of you who are studying integration at this time now let's move on to tangent squar the indefinite integral of tan squar is tangent x - x plus C likewise the indefinite integral of coent squ it's going to be not positive but negative Cent x - x + C the indefinite integral of secant squ is tangent x + C and the indefinite integral of cosecant squ is negative Cent x + C because the derivative of tangent is secant squ and the derivative of coent is negative cosecant squ so the integral of cosecant Square will be negative cotangent now there are some other trig formulas that you want to be familiar with this is called the reduction formulas in case you have higher Powers than two so the integral of sin n x DX is going to be -1 /n sin n -1 x cine X and then plus n -1 / n integral sin N - 2 X DX now you may need to know the integration by parts formula so if you're multiplying if you have two products it's integral UV which is UV minus integral VD for three products I have a formula for that in the form sheet now the reduction formula for cosine is this cosine n x DX is going to be 1 / n cosine n -1 x sin x + n -1 over an integral cosine N - 2 X DX now there's another one the integral of Tan N X DX it's going to be 1/ nus1 tangent nus1 of X and then minus the integral of tangent nus 2 X DX and N cannot equal 1 now there's some other reduction formulas for secant cosecant and coent but I'm going to put that in the formula sheet which you could find below so those are some common integration formulas for trick functions that uh you may encounter so feel free to take a look at that formula sheet when you get a chance and thanks again for watching