What is the integral of e^{4x}-5sin(x) ?

The integral of e^{4x}-5sin(x) is 1/4 e^{4x}+5cos(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{4x}-5sin(x)

\int e^{4 x} - 5 sin (x) d x

\frac{1}{4} e^{4 x} + 5 cos (x) + C

Solution steps

\int e^{4 x} - 5 sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{4 x} d x - \int 5 sin (x) d x

\int e^{4 x} d x = \frac{1}{4} e^{4 x}

\int 5 sin (x) d x = - 5 cos (x)

= \frac{1}{4} e^{4 x} - (- 5 cos (x))

Simplify

= \frac{1}{4} e^{4 x} + 5 cos (x)

Add a constant to the solution

= \frac{1}{4} e^{4 x} + 5 cos (x) + C

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

\int 3 x^{3} + 4 x^{2} - 5 x d x

x \to 0 lim (\frac{2 ( y + x ) - 2 y}{x})

\int 6 x^{2} + 4 x - 1 d x

\int \frac{10 x ^{3} - 5 x}{x ^{4} - x ^{2} + 6} d x

What is the integral of e^{4x}-5sin(x) ?
The integral of e^{4x}-5sin(x) is 1/4 e^{4x}+5cos(x)+C