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Popular >

integral of (1+t)e^t

Solution

\int (1 + t) e^{t} d t

Solution

e^{t} t + C

Solution steps

\int (1 + t) e^{t} d t

Apply Integration By Parts

: e^{t} (1 + t) - \int e^{t} d t

= e^{t} (1 + t) - \int e^{t} d t

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

= e^{t} (1 + t) - e^{t}

Simplify

e^{t} (1 + t) - e^{t} : e^{t} t

= e^{t} t

Add a constant to the solution

= e^{t} t + C

Popular Examples

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\int cot (x) csc^{4} (x) d x

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

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

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

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

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

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

integral of sin(c)

\int sin (c)

Frequently Asked Questions (FAQ)

What is the integral of (1+t)e^t ?
The integral of (1+t)e^t is e^tt+C