Integration using partial fractionsEdexcel International A Level Maths: Flashcards

What these 12 flashcards ask

\int\frac{1}{ax+b}\,dx?
\int\frac{2}{3x+5}\,dx?
\int\frac{3}{(x-1)^2}\,dx?
\int\frac{1}{(ax+b)^2}\,dx?
How do you split \frac{4x+5}{(x+1)(x+2)}?
What is the partial fraction form for (x+2)^2 in a denominator?
\frac{4x+5}{(x+1)(x+2)} in partial fractions?
Quick way to find A in a partial fraction?
Simplify \ln3+3\ln2.
Simplify 3\ln4+2\ln8-2\ln5.
Why is \int\frac{C}{(x+2)^2}\,dx not a logarithm?
\int0^2\frac{4x+5}{(x+1)(x+2)}\,dx?

Exam questions on Integration using partial fractions

Let $f(x)=\frac{4x+5}{(x+1)(x+2)}$ for $x>-1$ .
Hence find $\int_0^2f(x)\,dx$ , giving your answer in the form $\ln k$ .2 marks
A curve $C$ has gradient $\frac{dy}{dx}=\frac{2}{3x+5}+\frac{3}{(x-1)^2}$ for $x>1$ .
The curve $C$ passes through the point $(2,1)$ . Find the equation of $C$ .2 marks
Let $f(x)=\frac{5x+7}{(x-1)(x+3)}$ for $x>1$ .
Express $f(x)$ in partial fractions.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).