What is the integral of x^5sin(x^6+2) ?

The integral of x^5sin(x^6+2) is -1/6 cos(x^6+2)+C

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integral of x^5sin(x^6+2)

\int x^{5} sin (x^{6} + 2) d x

- \frac{1}{6} cos (x^{6} + 2) + C

Solution steps

\int x^{5} sin (x^{6} + 2) d x

Apply u-substitution

: \int \frac{sin ( u )}{6} d u

= \int \frac{sin ( u )}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{6} (- cos (u))

Substitute back

u = x^{6} + 2

= \frac{1}{6} (- cos (x^{6} + 2))

Simplify

= - \frac{1}{6} cos (x^{6} + 2)

Add a constant to the solution

= - \frac{1}{6} cos (x^{6} + 2) + C

x \to π lim (cot (x))

\int \frac{2 x ^{2} + 1}{( x - 3 ) ^{3}} d x

\int x (x + 5)^{2} d x

x y^{^{'}} = 1 - y^{2}

f (x) = - 2 ln (x)

What is the integral of x^5sin(x^6+2) ?
The integral of x^5sin(x^6+2) is -1/6 cos(x^6+2)+C