What is the integral of (x^3+cos(2x)) ?

The integral of (x^3+cos(2x)) is (x^4)/4+1/2 sin(2x)+C

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integral of (x^3+cos(2x))

\int (x^{3} + cos (2 x)) d x

\frac{x ^{4}}{4} + \frac{1}{2} sin (2 x) + C

Solution steps

\int x^{3} + 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^{3} d x + \int cos (2 x) d x

\int x^{3} d x = \frac{x ^{4}}{4}

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

= \frac{x ^{4}}{4} + \frac{1}{2} sin (2 x)

Add a constant to the solution

= \frac{x ^{4}}{4} + \frac{1}{2} sin (2 x) + C

f (θ) = 2 sin (θ)

\int_{1}^{e} 2 x ln (x) d x

\int \frac{2 sin ( ln ( x ) )}{x} d x

y^{3} - x y^{2} + x^{3} = 5, (1, 2)

\int x cosh (x) d x

What is the integral of (x^3+cos(2x)) ?
The integral of (x^3+cos(2x)) is (x^4)/4+1/2 sin(2x)+C