What is the integral of (cos(ax))/(sqrt(b+sin(ax))) ?

The integral of (cos(ax))/(sqrt(b+sin(ax))) is 2/a sqrt(b+sin(ax))+C

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integral of (cos(ax))/(sqrt(b+sin(ax)))

\int \frac{cos ( a x )}{b + sin ( a x )} d x

\frac{2}{a} b + sin (a x) + C

Solution steps

\int \frac{cos ( a x )}{b + sin ( a x )} d x

Apply u-substitution

: \int \frac{2}{a} d u

= \int \frac{2}{a} d u

Integral of a constant:

\int a d x = a x

= \frac{2}{a} u

Substitute back

u = b + sin (a x)

= \frac{2}{a} b + sin (a x)

Add a constant to the solution

= \frac{2}{a} b + sin (a x) + C

y^{^{''}} + 2 x y^{^{'}} = 0

\int sec^{2} (x t a) n^{3} x d x

\frac{d}{d x} (1 - 1 - x^{2})

\int \frac{x ^{2} - 1}{x ^{2} - 1} d x

\int x^{2} \cdot ab \cdot e^{- ab x + ab c} d x

What is the integral of (cos(ax))/(sqrt(b+sin(ax))) ?
The integral of (cos(ax))/(sqrt(b+sin(ax))) is 2/a sqrt(b+sin(ax))+C