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

The integral of x^3cos(h)x is 1/5 x^5cos(h)+C

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integral of x^3cos(h)x

\int x^{3} cos (h) x d x

\frac{1}{5} x^{5} cos (h) + C

Solution steps

\int x^{3} cos (h) x d x

Take the constant out:

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

= cos (h) \cdot \int x^{3} x d x

Simplify

x^{3} x : x^{4}

= cos (h) \cdot \int x^{4} d x

Apply the Power Rule

: \frac{x ^{5}}{5}

= cos (h) \frac{x ^{5}}{5}

Simplify

cos (h) \frac{x ^{5}}{5} : \frac{1}{5} x^{5} cos (h)

= \frac{1}{5} x^{5} cos (h)

Add a constant to the solution

= \frac{1}{5} x^{5} cos (h) + C

\frac{d}{d x} (x^{2} csc (5 x))

\int 6 sin (3 x + 1) d x

x \to \frac{1}{6} lim (∣ - 6 x + 1 ∣)

\frac{d}{d x} (x^{5} - 5 x^{4})

\frac{d}{d x} (\frac{x}{1 - 4 x ^{2}})

What is the integral of x^3cos(h)x ?
The integral of x^3cos(h)x is 1/5 x^5cos(h)+C