What is the integral of x+cos^2(x) ?

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

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integral of x+cos^2(x)

\int x + cos^{2} (x) d x

\frac{x ^{2}}{2} + \frac{1}{2} (x + \frac{1}{2} sin (2 x)) + C

Solution steps

\int x + cos^{2} (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 x d x + \int cos^{2} (x) d x

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

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

= \frac{x ^{2}}{2} + \frac{1}{2} (x + \frac{1}{2} sin (2 x))

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{1}{2} (x + \frac{1}{2} sin (2 x)) + C

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

\int 9 x - 4 d x

\int (x + 9)^{6} d x

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

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