Integration

Express $1(1+2x)(1−x)\frac{1}{(1+2x)(1-x)}$ in partial fractions.

[3]

Hence find the solution of the differential equation

(1+2x)(1-x)\frac{dy}{dx} = \tan y

for the interval $−12<x<710\displaystyle -\frac{1}{2} < x < \frac{7}{10}$ , given that $y=π6\displaystyle y = \frac{\pi}{6}$ when $x = 0$ .

Give your answer in the form $sin^n y = f(x)$ where $n\,$ is an integer to be found.

[7]

Express $1(1+2x)(1−x)\frac{1}{(1+2x)(1-x)}$ in partial fractions.

[3]

Hence find the solution of the differential equation

(1+2x)(1-x)\frac{dy}{dx} = \tan y

for the interval $−12<x<710\displaystyle -\frac{1}{2} < x < \frac{7}{10}$ , given that $y=π6\displaystyle y = \frac{\pi}{6}$ when $x = 0$ .

Give your answer in the form $sin^n y = f(x)$ where $n\,$ is an integer to be found.

Integration Questions