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

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

Popular >

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

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

- 2 cos (1 + x) + C

Solution steps

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

= 2 (- cos (1 + x))

Simplify

= - 2 cos (1 + x)

Add a constant to the solution

= - 2 cos (1 + x) + C

\int \frac{x + 1}{4 x} d x

f (x) = (1 + 5 x^{2}) (x - x^{2})

\int \frac{e ^{- 1 + x + l n (1 - x)}}{x ^{2}} d x

y^{^{'}} = - 6 x y

y^{^{'}} (x) = \frac{9 x ^{2}}{9 y ^{2} - 11}, y (1) = 0

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