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Popular >

integral of t+1/t

Solution

\int t + \frac{1}{t} d t

Solution

\frac{t ^{2}}{2} + ln ∣ t ∣ + C

Solution steps

\int t + \frac{1}{t} d t

Apply the Sum Rule:

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

= \int t d t + \int \frac{1}{t} d t

\int t d t = \frac{t ^{2}}{2}

\int \frac{1}{t} d t = ln ∣ t ∣

= \frac{t ^{2}}{2} + ln ∣ t ∣

Add a constant to the solution

= \frac{t ^{2}}{2} + ln ∣ t ∣ + C

Popular Examples

integral of (e^{x/2})/(sqrt(16-e^x))

\int \frac{e ^{\frac{x}{2}}}{16 - e ^{x}} d x

integral of 4x(2x^2+5)^6

\int 4 x (2 x^{2} + 5)^{6} d x

integral of (1+cos(x)+sin(x))/(cos(x))

\int \frac{1 + cos ( x ) + sin ( x )}{cos ( x )} d x

integral of (\sqrt[4]{x})/(sqrt(x)+1)

integral of 10xe^{2x}

\int 10 x e^{2 x} d x

Frequently Asked Questions (FAQ)

What is the integral of t+1/t ?
The integral of t+1/t is (t^2)/2+ln|t|+C