Solve \int t e^{a t^2} dt

Evaluate

\int t e^{a t^{2}} d t

Use the substitution d t = \frac{1}{2 a t} d v to transform the integral

More Steps

\int t e^{a t^{2}} \times \frac{1}{2 a t} d v

Simplify

More Steps

\int \frac{e ^{a t^{2}}}{2 a} d v

Use the substitution v = a t^{2} to transform the integral

\int \frac{e ^{v}}{2 a} d v

Rewrite the expression

\int \frac{1}{2 a} \times e^{v} d v

Use the property of integral \int k f (x) d x = k \int f (x) d x

\frac{1}{2 a} \times \int e^{v} d v

Use the property of integral \int e^{x} d x = e^{x}

\frac{1}{2 a} \times e^{v}

Multiply the terms

\frac{e ^{v}}{2 a}

Substitute back

\frac{e ^{a t^{2}}}{2 a}

Solution

\frac{e ^{a t^{2}}}{2 a} + C, C \in R

Evaluate the integral