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

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

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

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

- 2 cos (1 + x) + C

Solution steps

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

Apply Integration By Parts

: 2 x sin (1 + x) - \int cos (1 + x) d x

= 2 x sin (1 + x) - \int cos (1 + x) d x

\int cos (1 + x) d x = 2 (x sin (1 + x) + cos (1 + x))

= 2 x sin (1 + x) - 2 (x sin (1 + x) + cos (1 + x))

Simplify

2 x sin (1 + x) - 2 (x sin (1 + x) + cos (1 + x)) : - 2 cos (1 + x)

= - 2 cos (1 + x)

Add a constant to the solution

= - 2 cos (1 + x) + C

\int_{x}^{5} sin (t^{3}) d t

\int tan^{4} (9 x) d x

f (x) = \frac{2}{x} - \frac{1}{x ^{2}}

f (x) = \frac{x}{1 + x ^{2}}, (2, 0.4)

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