What is the integral of xcos(x^2+1) ?

The integral of xcos(x^2+1) is 1/2 sin(x^2+1)+C

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integral of xcos(x^2+1)

\int x cos (x^{2} + 1) d x

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

Solution steps

\int x cos (x^{2} + 1) d x

Apply u-substitution

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

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

Use the common integral:

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

= \frac{1}{2} sin (u)

Substitute back

u = x^{2} + 1

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

Add a constant to the solution

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

y^{^{''}} + 46 y^{^{'}} + 24 y = 0

\frac{d}{d x} (cot (x^{3}))

x \to 0 lim (+ (\frac{1}{x}))

(x^{2} - 1) y^{^{'}} + 2 x y^{2} = 0

\frac{d}{d θ} (6 cos (θ) cos (θ))

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