What is the integral of t^7sin(2t^4) ?

The integral of t^7sin(2t^4) is 1/16 (-2t^4cos(2t^4)+sin(2t^4))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of t^7sin(2t^4)

\int t^{7} sin (2 t^{4}) d t

\frac{1}{16} (- 2 t^{4} cos (2 t^{4}) + sin (2 t^{4})) + C

Solution steps

\int t^{7} sin (2 t^{4}) d t

Apply u-substitution

= \int \frac{u sin ( u )}{16} d u

Take the constant out:

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

= \frac{1}{16} \cdot \int u sin (u) d u

Apply Integration By Parts

= \frac{1}{16} (- u cos (u) - \int - cos (u) d u)

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

= \frac{1}{16} (- u cos (u) - (- sin (u)))

Substitute back

u = 2 t^{4}

= \frac{1}{16} (- 2 t^{4} cos (2 t^{4}) - (- sin (2 t^{4})))

Simplify

= \frac{1}{16} (- 2 t^{4} cos (2 t^{4}) + sin (2 t^{4}))

Add a constant to the solution

= \frac{1}{16} (- 2 t^{4} cos (2 t^{4}) + sin (2 t^{4})) + C

What is the integral of t^7sin(2t^4) ?
The integral of t^7sin(2t^4) is 1/16 (-2t^4cos(2t^4)+sin(2t^4))+C