What is the integral of x+5cos(x) ?

The integral of x+5cos(x) is (x^2)/2+5sin(x)+C

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integral of x+5cos(x)

\int x + 5 cos (x) d x

\frac{x ^{2}}{2} + 5 sin (x) + C

Solution steps

\int x + 5 cos (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 5 cos (x) d x

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

\int 5 cos (x) d x = 5 sin (x)

= \frac{x ^{2}}{2} + 5 sin (x)

Add a constant to the solution

= \frac{x ^{2}}{2} + 5 sin (x) + C

\int \frac{csc ^{5} ( ln ( x ) )}{x} d x

x \to 8 lim (x + 1)

f (x) = 8 x^{2} + x^{3}

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2} + 8})

\int 30 t - \frac{12}{t} d t

What is the integral of x+5cos(x) ?
The integral of x+5cos(x) is (x^2)/2+5sin(x)+C