What is the integral of 5e^x-cos(x)+3x^2-1/x ?

The integral of 5e^x-cos(x)+3x^2-1/x is 5e^x-sin(x)+x^3-ln|x|+C

Popular >

integral of 5e^x-cos(x)+3x^2-1/x

\int 5 e^{x} - cos (x) + 3 x^{2} - \frac{1}{x} d x

5 e^{x} - sin (x) + x^{3} - ln ∣ x ∣ + C

Solution steps

\int 5 e^{x} - cos (x) + 3 x^{2} - \frac{1}{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 5 e^{x} d x - \int cos (x) d x + \int 3 x^{2} d x - \int \frac{1}{x} d x

\int 5 e^{x} d x = 5 e^{x}

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= 5 e^{x} - sin (x) + x^{3} - ln ∣ x ∣

Add a constant to the solution

= 5 e^{x} - sin (x) + x^{3} - ln ∣ x ∣ + C

\int \frac{1}{x 36 x ^{2} - 4} d x

\frac{d}{d x} (x^{2} + 3 x + 2)

6 \cdot 6^{t} + 2 \cdot 2 t

\int \frac{sin ( 3 x )}{csc ^{2} ( 4 x )} d x

\frac{d y}{d x} = \frac{1 - y}{1 - x}

What is the integral of 5e^x-cos(x)+3x^2-1/x ?
The integral of 5e^x-cos(x)+3x^2-1/x is 5e^x-sin(x)+x^3-ln|x|+C