What is the integral of ((2-x^2)/x-sin(x)) ?

The integral of ((2-x^2)/x-sin(x)) is 2ln|x|-(x^2)/2+cos(x)+C

Popular >

integral of ((2-x^2)/x-sin(x))

\int (\frac{2 - x ^{2}}{x} - sin (x)) d x

2 ln ∣ x ∣ - \frac{x ^{2}}{2} + cos (x) + C

Solution steps

\int \frac{2 - x ^{2}}{x} - sin (x) 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{2 - x ^{2}}{x} d x - \int sin (x) d x

\int \frac{2 - x ^{2}}{x} d x = 2 ln ∣ x ∣ - \frac{x ^{2}}{2}

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

= 2 ln ∣ x ∣ - \frac{x ^{2}}{2} - (- cos (x))

Simplify

= 2 ln ∣ x ∣ - \frac{x ^{2}}{2} + cos (x)

Add a constant to the solution

= 2 ln ∣ x ∣ - \frac{x ^{2}}{2} + cos (x) + C

\int \frac{( 1 - x )}{9 - 4 x ^{2}} d x

\int sin (2 x) e^{s i n (x)} d x

\int 45 (1 + x^{2}) (7 + 15 x + 5 x^{3})^{16} d x

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

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

What is the integral of ((2-x^2)/x-sin(x)) ?
The integral of ((2-x^2)/x-sin(x)) is 2ln|x|-(x^2)/2+cos(x)+C