What is the integral of cos(x)+1/4 x ?

The integral of cos(x)+1/4 x is sin(x)+(x^2)/8+C

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integral of cos(x)+1/4 x

\int cos (x) + \frac{1}{4} x d x

sin (x) + \frac{x ^{2}}{8} + C

Solution steps

\int cos (x) + \frac{1}{4} 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 cos (x) d x + \int \frac{1}{4} x d x

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

\int \frac{1}{4} x d x = \frac{x ^{2}}{8}

= sin (x) + \frac{x ^{2}}{8}

Add a constant to the solution

= sin (x) + \frac{x ^{2}}{8} + C

\int \frac{1}{y - y ^{3}} d y

8 cos (t)

y^{^{'}} + 2 y = 3 e^{2 x}

\int_{0}^{4} 2 π (x) (4 x - x^{2}) d x

\frac{d}{d x} (\frac{1}{x ^{- 5}})

What is the integral of cos(x)+1/4 x ?
The integral of cos(x)+1/4 x is sin(x)+(x^2)/8+C