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

The integral of xsin(x^2+4) is -1/2 cos(x^2+4)+C

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integral of xsin(x^2+4)

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

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

Solution steps

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

Apply u-substitution

: \int \frac{sin ( u )}{2} d u

= \int \frac{sin ( u )}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{2} (- cos (u))

Substitute back

u = x^{2} + 4

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

Simplify

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

Add a constant to the solution

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

x \frac{d y}{d x} - 2 y = 6 x^{5}

y^{^{''}} + 6 y^{^{'}} + 9 y = 18 t^{2} + 24 t + 4

f (x) = \frac{1}{x + 5}

\int_{0}^{\frac{π}{2}} 5 cos^{2} (x) d x

\int \frac{9 x - 4}{x ^{3} - 4 x ^{2}} d x

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