What is the integral of 16e^{2x}+12x+11sin(x) ?

The integral of 16e^{2x}+12x+11sin(x) is 8e^{2x}+6x^2-11cos(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 16e^{2x}+12x+11sin(x)

\int 16 e^{2 x} + 12 x + 11 sin (x) d x

8 e^{2 x} + 6 x^{2} - 11 cos (x) + C

Solution steps

\int 16 e^{2 x} + 12 x + 11 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 16 e^{2 x} d x + \int 12 x d x + \int 11 sin (x) d x

\int 16 e^{2 x} d x = 8 e^{2 x}

\int 12 x d x = 6 x^{2}

\int 11 sin (x) d x = - 11 cos (x)

= 8 e^{2 x} + 6 x^{2} - 11 cos (x)

Add a constant to the solution

= 8 e^{2 x} + 6 x^{2} - 11 cos (x) + C

\int (x^{2} + 1)^{8} 2 x d x

\int - \frac{5}{1 + x ^{2}} d x

\int \frac{x - 2}{x ^{2} + 6 x + 8} d x

\int \frac{x + 1}{x ^{2} + 2 x + 25} d x

\int (1 + \frac{1}{2} u^{4} - \frac{2}{5} u^{9}) d u

What is the integral of 16e^{2x}+12x+11sin(x) ?
The integral of 16e^{2x}+12x+11sin(x) is 8e^{2x}+6x^2-11cos(x)+C