What is the integral of (2x+3)(x^2+3x+5)^4 ?

The integral of (2x+3)(x^2+3x+5)^4 is ((x^2+3x+5)^5)/5+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x+3)(x^2+3x+5)^4

\int (2 x + 3) (x^{2} + 3 x + 5)^{4} d x

\frac{( x ^{2} + 3 x + 5 ) ^{5}}{5} + C

Solution steps

\int (2 x + 3) (x^{2} + 3 x + 5)^{4} d x

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= \frac{u ^{5}}{5}

Substitute back

u = x^{2} + 3 x + 5

= \frac{( x ^{2} + 3 x + 5 ) ^{5}}{5}

Add a constant to the solution

= \frac{( x ^{2} + 3 x + 5 ) ^{5}}{5} + C

\int 6 x sin (2 - 3 x) d x

\int \frac{x ^{- 2}}{- 2} d x

\int t^{- 2} sin^{2} (1 + \frac{1}{t}) d t

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

\int (\frac{e ^{x} - 3 e ^{2 x}}{e ^{x}}) d x

What is the integral of (2x+3)(x^2+3x+5)^4 ?
The integral of (2x+3)(x^2+3x+5)^4 is ((x^2+3x+5)^5)/5+C