Show that the integral of tan (x) is ln|sec (x)| + C where C is a constant. First, recall that tan (x) can be rewritten in terms of sine and cosine. tan (x) = sin (x)/cos (x) The rephrasing of our question suggests …

Integrate (tanx)^2 Method: We use the trigonometric identity (tanx)^2 +1 = (secx)^2 to understand that (tanx)^2 can be written as (secx)^2-1.We then use the formula booklet to identify that (secx)^2 is a …

This is a question which tests your knowledge of how to use trigonometric identities as well as integration. As there is no way to immediately integrate tan^2 (x) ...

Integrate sec^2 (x)tan (X)dx This can be done with integration by substitution. If we let u=tanx then du/dx=sec^2 (X). If we substitute U into the integrand we get it being u (sec^2 (X))dx. rearranging the …

Firstly, use the trigonometric formula tan2x = sec2x - 1, which you can easily derive from sin 2 x + cos 2 x =1, by dividing both sides by cos 2 x and re-arranging. Now, you should remember that …

How to calculate the integral of sec (x)? First of all, multiply secx by (secx+tanx)/ (secx+tanx). Use the substitution u=secx+tanx, so that du= (secxtanx+sec 2 x) dx and then substitute both terms. …

So first we must rewrite the Integral as: I = - ∫ (-sin (x)) / (cos (x)) dx (Taking minus one outside of the integral) Now this is in the standard form and can be integrated;

given u = cos (x), therefore du/dx=-sin (x), as tan (x)=sin (x)/cos (x), can rewrite tan (x)= (-du/dx)/u, therefore integral can become [ (-1/u)du], after inegrating you are left with -ln (u)+c, therefore ln …

Find the integral of arctan (x) This is a complex question, the proof of which is unlikely to be asked at maths A-level, however the process behind the proof practices fundamental knowledge for the subject.

This is an example where we use integration by parts, but it is not immediately obvious where to start.Recall the integration by parts formula ∫u (dv/dx) dx = uv...