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Popular >

integral of 3e^x-1/x

Solution

\int 3 e^{x} - \frac{1}{x} d x

Solution

3 e^{x} - ln ∣ x ∣ + C

Solution steps

\int 3 e^{x} - \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 3 e^{x} d x - \int \frac{1}{x} d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

= 3 e^{x} - ln ∣ x ∣

Add a constant to the solution

= 3 e^{x} - ln ∣ x ∣ + C

Popular Examples

tangent of f(x)=sqrt(x^2+45),\at x=2 tangent of

f (x) = x^{2} + 45, at x = 2

integral from 0 to pi/2 of sin^7(x)

\int_{0}^{\frac{π}{2}} sin^{7} (x) d x

integral of (x^3+14)/(x^2+3x+2)

\int \frac{x ^{3} + 14}{x ^{2} + 3 x + 2} d x

simplify cos(sqrt(2t))simplify

cos (2 t)

(dy)/(dx)=y^2+1,y(4)=0

\frac{d y}{d x} = y^{2} + 1, y (4) = 0

Frequently Asked Questions (FAQ)

What is the integral of 3e^x-1/x ?
The integral of 3e^x-1/x is 3e^x-ln|x|+C