What is the integral of (4x+7)sin(4x) ?

The integral of (4x+7)sin(4x) is -xcos(4x)-7/4 cos(4x)+1/4 sin(4x)+C

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integral of (4x+7)sin(4x)

\int (4 x + 7) sin (4 x) d x

- x cos (4 x) - \frac{7}{4} cos (4 x) + \frac{1}{4} sin (4 x) + C

Solution steps

\int (4 x + 7) sin (4 x) d x

Apply Integration By Parts

: - x cos (4 x) - \frac{7}{4} cos (4 x) - \int - cos (4 x) d x

= - x cos (4 x) - \frac{7}{4} cos (4 x) - \int - cos (4 x) d x

\int - cos (4 x) d x = - \frac{1}{4} sin (4 x)

= - x cos (4 x) - \frac{7}{4} cos (4 x) - (- \frac{1}{4} sin (4 x))

Simplify

= - x cos (4 x) - \frac{7}{4} cos (4 x) + \frac{1}{4} sin (4 x)

Add a constant to the solution

= - x cos (4 x) - \frac{7}{4} cos (4 x) + \frac{1}{4} sin (4 x) + C

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

\int_{0}^{4} 2 π x (x) d x

\int (6 x)^{3} d x

n = 1 \sum \infty 4^{n} \cdot x^{n}

n = 1 \sum \infty \frac{1}{3 n + 1}

What is the integral of (4x+7)sin(4x) ?
The integral of (4x+7)sin(4x) is -xcos(4x)-7/4 cos(4x)+1/4 sin(4x)+C