What is the integral of x^3cos(x^4+2) ?

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

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integral of x^3cos(x^4+2)

\int x^{3} cos (x^{4} + 2) d x

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

Solution steps

\int x^{3} cos (x^{4} + 2) d x

Apply u-substitution

: \int \frac{cos ( u )}{4} d u

= \int \frac{cos ( u )}{4} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{4} sin (u)

Substitute back

u = x^{4} + 2

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

Add a constant to the solution

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

\int_{0}^{3} \frac{3 t}{( t - 4 ) ^{2}} d t

\frac{d}{d x} (2 x + 7 + \frac{450}{x})

f (x) = \frac{2}{3} (x^{2} + 1)^{\frac{3}{2}}

y^{^{''}} + y = 0, y (\frac{π}{3}) = 0, y^{^{'}} (\frac{π}{3}) = 6

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

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