What is the integral of 5xsin(x^2) ?

The integral of 5xsin(x^2) is -5/2 cos(x^2)+C

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integral of 5xsin(x^2)

\int 5 x sin (x^{2}) d x

- \frac{5}{2} cos (x^{2}) + C

Solution steps

\int 5 x sin (x^{2}) d x

Take the constant out:

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

= 5 \cdot \int x sin (x^{2}) d x

Apply u-substitution

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

= 5 \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

= 5 \cdot \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

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

= 5 \cdot \frac{1}{2} (- cos (u))

Substitute back

u = x^{2}

= 5 \cdot \frac{1}{2} (- cos (x^{2}))

Simplify

5 \cdot \frac{1}{2} (- cos (x^{2})) : - \frac{5}{2} cos (x^{2})

= - \frac{5}{2} cos (x^{2})

Add a constant to the solution

= - \frac{5}{2} cos (x^{2}) + C

\int cos (3 x y) d x

x \to 0 + lim (x (2))

x \to 0 lim (e^{x} cos (3 x))

\int \frac{1}{e ^{2 x} - 3 e ^{x}} d x

\frac{d}{d t} (tan (3 t))

What is the integral of 5xsin(x^2) ?
The integral of 5xsin(x^2) is -5/2 cos(x^2)+C