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Popular >

integral of (te^t+t)

Solution

\int (t e^{t} + t) d t

Solution

e^{t} t - e^{t} + \frac{t ^{2}}{2} + C

Solution steps

\int t e^{t} + 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 e^{t} d t + \int t d t

\int t e^{t} d t = e^{t} t - e^{t}

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

= e^{t} t - e^{t} + \frac{t ^{2}}{2}

Add a constant to the solution

= e^{t} t - e^{t} + \frac{t ^{2}}{2} + C

Popular Examples

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

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

integral of (x^2)/(x^4+4)

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

integral of 1/((x+1)sqrt(x^2+2x+3))

\int \frac{1}{( x + 1 ) x ^{2} + 2 x + 3} d x

integral of e^{-x}tan(3+2e^{-x})

\int e^{- x} tan (3 + 2 e^{- x}) d x

integral of (2x-2)/((x-1)^3+4(x-1))

\int \frac{2 x - 2}{( x - 1 ) ^{3} + 4 ( x - 1 )} d x

Frequently Asked Questions (FAQ)

What is the integral of (te^t+t) ?
The integral of (te^t+t) is e^tt-e^t+(t^2)/2+C