What is the integral of (5x+7)^4 ?

The integral of (5x+7)^4 is 1/25 (5x+7)^5+C

Popular >

integral of (5x+7)^4

\int (5 x + 7)^{4} d x

\frac{1}{25} (5 x + 7)^{5} + C

Solution steps

\int (5 x + 7)^{4} d x

Apply u-substitution

: \int \frac{u ^{4}}{5} d u

= \int \frac{u ^{4}}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int u^{4} d u

Apply the Power Rule

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

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

Substitute back

u = 5 x + 7

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

Simplify

\frac{1}{5} \cdot \frac{( 5 x + 7 ) ^{5}}{5} : \frac{1}{25} (5 x + 7)^{5}

= \frac{1}{25} (5 x + 7)^{5}

Add a constant to the solution

= \frac{1}{25} (5 x + 7)^{5} + C

\int e^{0.03 x} d x

\int (x^{4} - 5 x^{2} - 6 x)^{4} (4 x^{3} - 10 x - 6) d x

\int \frac{8 x - 11}{5 + 2 x - x ^{2}} d x

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

\int \frac{( 4 x + 5 )}{x ^{2} + 4 x + 20} d x