What is the integral of (2x+7)^4 ?

The integral of (2x+7)^4 is 1/10 (2x+7)^5+C

Popular >

integral of (2x+7)^4

\int (2 x + 7)^{4} d x

\frac{1}{10} (2 x + 7)^{5} + C

Solution steps

\int (2 x + 7)^{4} d x

Apply u-substitution

: \int \frac{u ^{4}}{2} d u

= \int \frac{u ^{4}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u^{4} d u

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{u ^{5}}{5}

Substitute back

u = 2 x + 7

= \frac{1}{2} \cdot \frac{( 2 x + 7 ) ^{5}}{5}

Simplify

\frac{1}{2} \cdot \frac{( 2 x + 7 ) ^{5}}{5} : \frac{1}{10} (2 x + 7)^{5}

= \frac{1}{10} (2 x + 7)^{5}

Add a constant to the solution

= \frac{1}{10} (2 x + 7)^{5} + C

\int \frac{2 x ^{3}}{x ^{4} - 1} d x

\int \frac{x ^{5}}{( 1 + x ^{3} ) ^{\frac{3}{2}}} d x

\int (x^{2} + 2 x + 1) sin (3 x) d x

\int \frac{x ^{2}}{8 + x} d x

\int \frac{x}{x ^{\frac{2}{3}} + x ^{\frac{8}{6}}} d x