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Popular >

integral of xsin(x^2+1)

Solution

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

Solution

- \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

Popular Examples

integral of (3n-4)/(n^2-2n)

\int \frac{3 n - 4}{n ^{2} - 2 n}

integral of ((1+xy)e^{xy})

\int ((1 + x y) e^{x y}) d x

tangent of y-x^2y=2-2x^3 tangent of

y - x^{2} y = 2 - 2 x^{3}

integral of 7/(x^2sqrt(x^2+25))

\int \frac{7}{x ^{2} x ^{2} + 25} d x

(dy)/(dx)=(y-1)^2

\frac{d y}{d x} = (y - 1)^{2}

Frequently Asked Questions (FAQ)

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