What is the integral of (2t^3-1/(3x)+e^{2x}+cos(x)) ?

The integral of (2t^3-1/(3x)+e^{2x}+cos(x)) is sin(x)-1/3 ln|x|+1/2 e^{2x}+2t^3x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2t^3-1/(3x)+e^{2x}+cos(x))

\int (2 t^{3} - \frac{1}{3 x} + e^{2 x} + cos (x)) d x

sin (x) - \frac{1}{3} ln ∣ x ∣ + \frac{1}{2} e^{2 x} + 2 t^{3} x + C

Solution steps

\int 2 t^{3} - \frac{1}{3 x} + e^{2 x} + cos (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 cos (x) d x - \int \frac{1}{3 x} d x + \int e^{2 x} d x + \int 2 t^{3} d x

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

\int \frac{1}{3 x} d x = \frac{1}{3} ln ∣ x ∣

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

\int 2 t^{3} d x = 2 t^{3} x

= sin (x) - \frac{1}{3} ln ∣ x ∣ + \frac{1}{2} e^{2 x} + 2 t^{3} x

Add a constant to the solution

= sin (x) - \frac{1}{3} ln ∣ x ∣ + \frac{1}{2} e^{2 x} + 2 t^{3} x + C

\int 2 sin^{7} (x) cos (x) d x

\int (\frac{3 x ^{3} - 2 x ^{5}}{x ^{2}}) d x

\int 4 tan^{3} (x) sec^{3} (x) d x

\int \frac{3}{8 + 7 cos ( x )} d x

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

What is the integral of (2t^3-1/(3x)+e^{2x}+cos(x)) ?
The integral of (2t^3-1/(3x)+e^{2x}+cos(x)) is sin(x)-1/3 ln|x|+1/2 e^{2x}+2t^3x+C