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

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

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

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

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

Solution steps

\int x sin (x^{2} + 1) 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} + 1

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (e^{\frac{- x ^{2}}{2}})

2 x + \frac{4 x}{3 x - 1}

x \to 3 lim (\frac{2 x + 3}{x - 3})

2 sec (2 x)

n = 1 \sum \infty lo g_{e} (\frac{n}{n + 1})

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