What is the integral of (4x+2)sin(x^2+x+2) ?

The integral of (4x+2)sin(x^2+x+2) is -2cos(x^2+x+2)+C

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integral of (4x+2)sin(x^2+x+2)

\int (4 x + 2) sin (x^{2} + x + 2) d x

- 2 cos (x^{2} + x + 2) + C

Solution steps

\int (4 x + 2) sin (x^{2} + x + 2) d x

Apply u-substitution

: \int 2 sin (u) d u

= \int 2 sin (u) d u

Take the constant out:

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

= 2 \cdot \int sin (u) d u

Use the common integral:

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

= 2 (- cos (u))

Substitute back

u = x^{2} + x + 2

= 2 (- cos (x^{2} + x + 2))

Simplify

= - 2 cos (x^{2} + x + 2)

Add a constant to the solution

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

\frac{d}{d x} (arcsin (7 x^{5}))

f (x) = 3 x + x^{2}

\int x^{\frac{1}{3}} (x^{\frac{4}{3}} + 9)^{8} d x

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

\frac{1}{s ^{2} + 1}

What is the integral of (4x+2)sin(x^2+x+2) ?
The integral of (4x+2)sin(x^2+x+2) is -2cos(x^2+x+2)+C