What is the integral of 300te^{(-t^2)/7} ?

The integral of 300te^{(-t^2)/7} is -1050e^{-(t^2)/7}+C

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integral of 300te^{(-t^2)/7}

\int 300 t e^{\frac{- t ^{2}}{7}} d t

- 1050 e^{- \frac{t ^{2}}{7}} + C

Solution steps

\int 300 t e^{\frac{- t ^{2}}{7}} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 300 \cdot \int t e^{\frac{- t ^{2}}{7}} d t

Simplify

= 300 \cdot \int e^{- \frac{t ^{2}}{7}} t d t

Apply u-substitution

: \int - \frac{7 e ^{u}}{2} d u

= 300 \cdot \int - \frac{7 e ^{u}}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 300 (- \frac{7}{2} \cdot \int e^{u} d u)

Use the common integral:

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

= 300 (- \frac{7}{2} e^{u})

Substitute back

u = - \frac{t ^{2}}{7}

= 300 (- \frac{7}{2} e^{- \frac{t ^{2}}{7}})

Simplify

300 (- \frac{7}{2} e^{- \frac{t ^{2}}{7}}) : - 1050 e^{- \frac{t ^{2}}{7}}

= - 1050 e^{- \frac{t ^{2}}{7}}

Add a constant to the solution

= - 1050 e^{- \frac{t ^{2}}{7}} + C

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What is the integral of 300te^{(-t^2)/7} ?
The integral of 300te^{(-t^2)/7} is -1050e^{-(t^2)/7}+C