Question

Sec x/1+sin^2x
Integrate from 0 to π/4
Pls help in solving this

Answer 1

so,
we can try the substitution, \( \large u = \sin x\)

and before that, we can do some manipulation,

\(\Large \dfrac{\sec x}{(1+\sin^2 x)} = \dfrac{1}{\cos x(1+\sin^2 x)}\)

\(\Large \dfrac{\cos x}{\cos^2 x(1+\sin^2 x)} = \dfrac{\cos x}{(1-\sin^2 cx)(1+\sin^2 x)}\)

Answer 2

and now we can happily substitute u = sin x

Answer 3

let me know if you need hint in solving
\(\Large \dfrac{1}{(1-u^2)(1+u^2 )}\)

Answer 4

Am not getting the first step where
Cosx cos^2 x came from

Answer 5

sec x = 1/cos x

now i wanted cos^2 x in the denominator

so I multiplied numerator and denominator by cos x

Answer 6

Thanks. Misunderstanding

Answer 7

np B)

Answer 8

you could solve it entirely? :)

Answer 9

Am not getting the first step where
Cosx cos^2 x came from

Answer 10

huh?