What is the integral of (x-1)cos(5x) ?

The integral of (x-1)cos(5x) is 1/5 sin(5x)(x-1)+1/25 cos(5x)+C

Popular >

integral of (x-1)cos(5x)

\int (x - 1) cos (5 x) d x

\frac{1}{5} sin (5 x) (x - 1) + \frac{1}{25} cos (5 x) + C

Solution steps

\int (x - 1) cos (5 x) d x

Apply Integration By Parts

: \frac{1}{5} sin (5 x) (x - 1) - \int \frac{1}{5} sin (5 x) d x

= \frac{1}{5} sin (5 x) (x - 1) - \int \frac{1}{5} sin (5 x) d x

\int \frac{1}{5} sin (5 x) d x = - \frac{1}{25} cos (5 x)

= \frac{1}{5} sin (5 x) (x - 1) - (- \frac{1}{25} cos (5 x))

Simplify

= \frac{1}{5} sin (5 x) (x - 1) + \frac{1}{25} cos (5 x)

Add a constant to the solution

= \frac{1}{5} sin (5 x) (x - 1) + \frac{1}{25} cos (5 x) + C

\int cos (\frac{t}{4}) d t

\int (\frac{3}{4 x + 5} - \frac{1}{e ^{3 x}} + 3^{4 x}) d x

\int (x^{3} + x)^{5} (3 x^{2} + 1) d x

\int \frac{6}{x ln ^{3} ( 4 x )} d x

\int 12 (x^{4} + 4 x^{2} + 1)^{2} (x^{3} + 2 x) d x

What is the integral of (x-1)cos(5x) ?
The integral of (x-1)cos(5x) is 1/5 sin(5x)(x-1)+1/25 cos(5x)+C