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

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

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

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

- 2 cos (x + 1) + C

Solution steps

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

= 2 (- cos (x + 1))

Simplify

= - 2 cos (x + 1)

Add a constant to the solution

= - 2 cos (x + 1) + C

\int_{1}^{e} \frac{ln ( x )}{x} d x

(1 + 6 x^{2}) (x - x^{2})

x \to \infty lim (- 3 x^{2})

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (0) = b, y^{^{'}} (0) = 2

\frac{\partial}{\partial x} (cos (2 (2 y x - 1)))

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