en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(Inx)

Solution

\int sin (I n x) d x

Solution

- \frac{1}{I n} cos (I n x) + C

Solution steps

\int sin (I n x) d x

Apply u-substitution

: \int \frac{sin ( u )}{I n} d u

= \int \frac{sin ( u )}{I n} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{I n} (- cos (u))

Substitute back

u = I n x

= \frac{1}{I n} (- cos (I n x))

Simplify

= - \frac{1}{I n} cos (I n x)

Add a constant to the solution

= - \frac{1}{I n} cos (I n x) + C

Popular Examples

integral of cos(x)[sin(x)+1]^3

\int cos (x) [sin (x) + 1]^{3} d x

integral of x/(1+x^6)

\int \frac{x}{1 + x ^{6}} d x

integral of-9x^3e^{x^4}

\int - 9 x^{3} e^{x^{4}} d x

integral of 8/(x^4-16)

\int \frac{8}{x ^{4} - 16} d x

integral of (x^4)/((sqrt(25-x^2))^3)

\int \frac{x ^{4}}{( 25 - x ^{2} ) ^{3}} d x

Frequently Asked Questions (FAQ)

What is the integral of sin(Inx) ?
The integral of sin(Inx) is -1/(In)cos(Inx)+C