What is the integral of (sin(sqrt(1+x)))/(sqrt(1+x)) ?

The integral of (sin(sqrt(1+x)))/(sqrt(1+x)) is -2cos(sqrt(1+x))+C

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integral of (sin(sqrt(1+x)))/(sqrt(1+x))

\int \frac{sin ( 1 + x )}{1 + x} d x

- 2 cos (1 + x) + C

Solution steps

\int \frac{sin ( 1 + x )}{1 + x} d x

Apply u-substitution

: \int 2 sin (u) d u

= \int 2 sin (u) d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= 2 (- cos (u))

Substitute back

u = 1 + x

= 2 (- cos (1 + x))

Simplify

= - 2 cos (1 + x)

Add a constant to the solution

= - 2 cos (1 + x) + C

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

\int 2 t + 3 d t

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

(x - 3) x (x + 3), 3 - x, 0, 2

y = - (x + \frac{1}{2})^{2} + \frac{7}{2}

What is the integral of (sin(sqrt(1+x)))/(sqrt(1+x)) ?
The integral of (sin(sqrt(1+x)))/(sqrt(1+x)) is -2cos(sqrt(1+x))+C