Question

Integrate
$\huge\green\tt\frac{ \sqrt{tanx} }{sinxcosx}$​

Answer 1

The functions of the blood are:

Transport of digested food from the alimentary canal to tissues. These substances are simple sugars like glucose, amino acids, vitamins, mineral salts, etc.

Transport of oxygen in the form of an unstable compound ‘oxyhaemoglobin’ from the lungs to the tissues.

Transport of carbon dioxide from the tissues to the lungs.

Transport of excretory materials from the tissues to the liver, kidney or the skin for elimination.

Distribution of hormones from glands to the target sites.

Distribution of heat to keep the body temperature uniform.

Answer 2

Answer:

Mate answer is here!!

Step-by-step explanation:

I = ( 1 + sinx)dx /( sinx + sinx .cosx)

we Know ,

sin2x = 2tanx/( 1+ tan²x)

cos2x = (1 - tan²x)/( 1 + tan²x)

use this

I = { 1 + 2tanx/2/( 1+ tan²x/2)}dx/{ 2tanx/2/( 1+tan²/2.) + 2tanx/2( 1 - tan²x/2)/( 1+ tan²x/2)² }

= ( 1 + tan²x/2 +2tanx/2)dx/( 2tanx/2)( 1+ tan²x/2 + 1 - tan²x/2)/( 1 + tan²x/2)

= ( 1 + tan²x/2)( 1 + tanx/2)²dx/2tanx/2× 2

= (1/4) { (sec²x/2)( 1 +tanx/2)dx/tanx/2

[ note :- ( 1 + tan²x/2 ) = sec²x/2 ]

now , let tanx/2 = P

differentiate

sec²x/2 × 1/2 dx = dP

sec²x/2dx = 2dP

use this in above

I = ( 1 + P)²2.dP/4P

=1/2 × ( 1+P² + 2P)dP/P

=1/2 × { dP/P + P.dP + 2dP }

= 1/2× { lnP + P²/2 + 2P }

put P = tanx/2

I = 1/2tanx/2 + 1/4tan²x/2 + tanx + C.