What is the integral of x^9e^{7x^5} ?

The integral of x^9e^{7x^5} is 1/245 (e^{7x^5}*7x^5-e^{7x^5})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^9e^{7x^5}

\int x^{9} e^{7 x^{5}} d x

\frac{1}{245} (e^{7 x^{5}} \cdot 7 x^{5} - e^{7 x^{5}}) + C

Solution steps

\int x^{9} e^{7 x^{5}} d x

Apply u-substitution

: \int \frac{e ^{u} u}{245} d u

= \int \frac{e ^{u} u}{245} d u

Take the constant out:

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

= \frac{1}{245} \cdot \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= \frac{1}{245} (e^{u} u - \int e^{u} d u)

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

= \frac{1}{245} (e^{u} u - e^{u})

Substitute back

u = 7 x^{5}

= \frac{1}{245} (e^{7 x^{5}} \cdot 7 x^{5} - e^{7 x^{5}})

Add a constant to the solution

= \frac{1}{245} (e^{7 x^{5}} \cdot 7 x^{5} - e^{7 x^{5}}) + C

\int x^{3} - 2 x + 2 d x

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

\int lo g_{4} (3 x + 1) d x

3 y^{^{''}} + 2 y^{^{'}} - y = 0

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

What is the integral of x^9e^{7x^5} ?
The integral of x^9e^{7x^5} is 1/245 (e^{7x^5}*7x^5-e^{7x^5})+C