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

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

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integral of x*cos(x^2+1)

\int x \cdot 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

\int \frac{3 x - 1}{4 x ^{2} - 4 x + 17} d x

\frac{d y}{d x} = \frac{( 3 - y )}{2 x}

100 y^{^{''}} + 20 y^{^{'}} + y = 0

\int - x^{- 3} d x

x \to 1 + lim (x - 2)

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