What is the integral of 6xcos(7x) ?

The integral of 6xcos(7x) is 6/49 (7xsin(7x)+cos(7x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 6xcos(7x)

\int 6 x cos (7 x) d x

\frac{6}{49} (7 x sin (7 x) + cos (7 x)) + C

Solution steps

\int 6 x cos (7 x) d x

Take the constant out:

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

= 6 \cdot \int x cos (7 x) d x

Apply u-substitution

: \int \frac{u cos ( u )}{49} d u

= 6 \cdot \int \frac{u cos ( u )}{49} d u

Take the constant out:

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

= 6 \cdot \frac{1}{49} \cdot \int u cos (u) d u

Apply Integration By Parts

: u sin (u) - \int sin (u) d u

= 6 \cdot \frac{1}{49} (u sin (u) - \int sin (u) d u)

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

= 6 \cdot \frac{1}{49} (u sin (u) - (- cos (u)))

Substitute back

u = 7 x

= 6 \cdot \frac{1}{49} (7 x sin (7 x) - (- cos (7 x)))

Simplify

6 \cdot \frac{1}{49} (7 x sin (7 x) - (- cos (7 x))) : \frac{6}{49} (7 x sin (7 x) + cos (7 x))

= \frac{6}{49} (7 x sin (7 x) + cos (7 x))

Add a constant to the solution

= \frac{6}{49} (7 x sin (7 x) + cos (7 x)) + C

\int x [cosh^{2} (2 x^{2}) - sinh^{2} (2 x^{2})] d x

\int \frac{x + 5}{( x + 2 ) ( x ^{2} - 2 x + 2 ) ^{2}} d x

\int x^{5} 4 x^{2} - 1 d x

\int 6 x x^{2} - 1 d x

\int 110 \cdot \frac{3 - ln ( x )}{x ^{2}} d x

What is the integral of 6xcos(7x) ?
The integral of 6xcos(7x) is 6/49 (7xsin(7x)+cos(7x))+C