What is the integral of 3xsin(x^2) ?

The integral of 3xsin(x^2) is -3/2 cos(x^2)+C

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integral of 3xsin(x^2)

\int 3 x sin (x^{2}) d x

- \frac{3}{2} cos (x^{2}) + C

Solution steps

\int 3 x sin (x^{2}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int x sin (x^{2}) d x

Apply u-substitution

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

= 3 \cdot \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

= 3 \cdot \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

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

= 3 \cdot \frac{1}{2} (- cos (u))

Substitute back

u = x^{2}

= 3 \cdot \frac{1}{2} (- cos (x^{2}))

Simplify

3 \cdot \frac{1}{2} (- cos (x^{2})) : - \frac{3}{2} cos (x^{2})

= - \frac{3}{2} cos (x^{2})

Add a constant to the solution

= - \frac{3}{2} cos (x^{2}) + C

y^{^{'''}} + 6 y^{^{''}} + 9 y^{^{'}} = 0

\int_{1}^{6} \frac{2}{x - 11} d x

\frac{d x}{d t} + 4 \cdot 1 0^{- 4} x = 8 \cdot 1 0^{- 5}, x (0) = 1

f (x) = 3 x^{2} - 5 x + 1

(4 x - 3)^{\frac{1}{2}}

What is the integral of 3xsin(x^2) ?
The integral of 3xsin(x^2) is -3/2 cos(x^2)+C