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

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

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integral of x^1sin(x^2)

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

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

Solution steps

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

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

Simplify

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

Add a constant to the solution

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

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

\int x^{2} sec (x^{3}) tan (x^{3}) d x

4 x^{2}

\int sin^{7} (x) cos^{10} (x) d x

\int x \cdot (2 x + 5)^{10} d x

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