What is the integral of+(2ax+b)(ax^2+bx)^7 ?

The integral of+(2ax+b)(ax^2+bx)^7 is ((ax^2+bx)^8)/8+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of+(2ax+b)(ax^2+bx)^7

\int + (2 a x + b) (a x^{2} + b x)^{7} d x

\frac{( a x ^{2} + b x ) ^{8}}{8} + C

Solution steps

\int (2 a x + b) (a x^{2} + b x)^{7} d x

Apply u-substitution

: \int u^{7} d u

= \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= \frac{u ^{8}}{8}

Substitute back

u = a x^{2} + b x

= \frac{( a x ^{2} + b x ) ^{8}}{8}

Add a constant to the solution

= \frac{( a x ^{2} + b x ) ^{8}}{8} + C

\int x^{\frac{- 4}{6}} d x

\int \frac{5 ^{t a n (x)}}{cos ^{2} ( x )} d x

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

\int e^{k x} sin (x) d x

\int \frac{y ^{3}}{2 y - 1} d y

What is the integral of+(2ax+b)(ax^2+bx)^7 ?
The integral of+(2ax+b)(ax^2+bx)^7 is ((ax^2+bx)^8)/8+C