What is the integral of 5xcos(4x^2+2) ?

The integral of 5xcos(4x^2+2) is 5/8 sin(4x^2+2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5xcos(4x^2+2)

\int 5 x cos (4 x^{2} + 2) d x

\frac{5}{8} sin (4 x^{2} + 2) + C

Solution steps

\int 5 x cos (4 x^{2} + 2) d x

Take the constant out:

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

= 5 \cdot \int x cos (4 x^{2} + 2) d x

Apply u-substitution

: \int \frac{cos ( u )}{8} d u

= 5 \cdot \int \frac{cos ( u )}{8} d u

Take the constant out:

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

= 5 \cdot \frac{1}{8} \cdot \int cos (u) d u

Use the common integral:

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

= 5 \cdot \frac{1}{8} sin (u)

Substitute back

u = 4 x^{2} + 2

= 5 \cdot \frac{1}{8} sin (4 x^{2} + 2)

Simplify

5 \cdot \frac{1}{8} sin (4 x^{2} + 2) : \frac{5}{8} sin (4 x^{2} + 2)

= \frac{5}{8} sin (4 x^{2} + 2)

Add a constant to the solution

= \frac{5}{8} sin (4 x^{2} + 2) + C

\int 2 y sin (x) - x sin (y) d y

\int \frac{6}{7 x} d x

\int (1 + 4 x) d x

\int 12 csc^{2} (6 x) cot (6 x) d x

\int \frac{1}{1 + e ^{2}} d x

What is the integral of 5xcos(4x^2+2) ?
The integral of 5xcos(4x^2+2) is 5/8 sin(4x^2+2)+C