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

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

Popular >

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

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

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

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{1}{x} d x = 2 x

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

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

Add a constant to the solution

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

\int (1 + 2 y)^{2} d y

\int \frac{1}{x ^{2} + 5 x - 14} d x

\int \frac{e ^{t}}{e ^{t} + 4} d t

\int \frac{( 1 + x ) ^{2}}{x ^{2}} d x

\int \frac{1}{( x ^{2} + 4 ) ^{3}} d x

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