Question

integrate sec 4/9 theta cosec^ 14/9 theta d theta

Answer 1

5/34 is the answer for your question

Answer 2

given,

$\int \left(sec\frac{4}{9}\theta \right)\:\left(cosec\:\frac{14}{9}\theta \right)\:d\theta \\\\solution:\\=\int \left(sec\frac{4}{9}\theta \right)\:\left(cosec\:\frac{14}{9}\theta \right)\:d\theta \\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=sec(\frac{4}{9})csc(\frac{14}{9}).\int\left \rigtd\theta \theta d\theta$

$=\frac{1}{cos(\frac{4}{9} )sin(\frac{14}{9}) } \int\theta\theta d\theta\\=\frac{1}{cos(\frac{4}{9} )sin(\frac{14}{9}) } \int\theta^2 d\theta\\\\=\frac{1}{cos(\frac{4}{9} )sin(\frac{14}{9}) } \int\theta^3/3\\\\=\frac{\theta^3}{cos(\frac{4}{9} )sin(\frac{14}{9}) } +C$