Integration of Trigonometric Identities | P3

KEYPOINTS:

\(\int\) e^{ax + b} dx = \(\frac{1}{a}\)e^{ax + b} + C
\(\int\) sin(ax + b) dx = –\(\frac{1}{a}\)cos(ax + b) + C
\(\int\) cos(ax + b) dx = \(\frac{1}{a}\)sin(ax + b) + C
\(\int\) sec²(ax + b) dx = \(\frac{1}{a}\)tan(ax + b) + C
\(\int\) \(\frac{1}{x}\) dx = ln|x| + C
\(\int\) \(\frac{1}{ax + b}\) dx = \(\frac{1}{a}\)ln|ax + b| + C
\(\int\) \(\frac{1}{1 + x^2}\) dx = tan^–1x + C
\(\int\) \(\frac{1}{1+b^2x^2}\) dx = \(\frac{1}{b}\) tan^–1(bx) + C
\(\int\) \(\frac{1}{x^2 + a^2}\) dx = \(\frac{1}{a}\)tan^–1(\(\frac{x}{a}\)) + C
\(\int\) \(\frac{1}{x^2 – a^2}\) dx = \(\frac{1}{2a}\)ln (\(\frac{x–a}{x+a}\)) + C
\(\int\) \(\frac{1}{a^2 – x^2}\) dx = \(\frac{1}{2a}\)ln (\(\frac{a+x}{a–x}\)) + C
\(\int\) \(\frac{f’(x)}{f(x)}\) dx = ln(f(x)) + C

CAIE: A Level - Mathematics 9709 - Pure Mathematics 3