What is the integral of na^{cos(bx)}sin(bx) ?

The integral of na^{cos(bx)}sin(bx) is -na^{cos(bx)} 1/(bln(a))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of na^{cos(bx)}sin(bx)

\int n a^{c o s (b x)} sin (b x) d x

- n a^{c o s (b x)} \frac{1}{b ln ( a )} + C

Solution steps

\int n a^{c o s (b x)} sin (b x) d x

Take the constant out:

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

= n \cdot \int sin (b x) a^{c o s (b x)} d x

Apply u-substitution

: \int - \frac{1}{b ln ( a )} d u

= n \cdot \int - \frac{1}{b ln ( a )} d u

Integral of a constant:

\int a d x = a x

= n (- \frac{1}{b ln ( a )}) u

Substitute back

u = a^{c o s (b x)}

= n (- \frac{1}{b ln ( a )}) a^{c o s (b x)}

Simplify

= - n a^{c o s (b x)} \frac{1}{b ln ( a )}

Add a constant to the solution

= - n a^{c o s (b x)} \frac{1}{b ln ( a )} + C

\int 9 x e^{- 4 x^{2}} d x

\int s 1 0^{s^{2}} d s

\int \frac{6 x + 6}{x ^{2} + 1} d x

\int cot^{3} (2 t) d t

\int (x + 4)^{2} (x - 6)^{5} (x - 9)^{3} d x

What is the integral of na^{cos(bx)}sin(bx) ?
The integral of na^{cos(bx)}sin(bx) is -na^{cos(bx)} 1/(bln(a))+C