What is the integral of x^3cos(x^4+1) ?

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

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integral of x^3cos(x^4+1)

\int x^{3} cos (x^{4} + 1) d x

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

Solution steps

\int x^{3} cos (x^{4} + 1) 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} + 1

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

Add a constant to the solution

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

\int (6 + x^{9})^{5} x^{8} d x

h \to \infty lim (\frac{3 h + 2 x h ^{2} + x ^{2} + h ^{3}}{4 - 3 x h - 2 x ^{3} h ^{3}})

\frac{d}{d x} (e^{6 x s i n (2 x)})

x \to 3 lim (sin (\frac{1}{x - 3}))

\frac{d}{d x} ((x^{2} + 5)^{\frac{1}{2}})

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