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

The integral of (4x+5)^5 is 1/24 (4x+5)^6+C

Popular >

integral of (4x+5)^5

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

\frac{1}{24} (4 x + 5)^{6} + C

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{1}{4} \cdot \frac{u ^{6}}{6}

Substitute back

u = 4 x + 5

= \frac{1}{4} \cdot \frac{( 4 x + 5 ) ^{6}}{6}

Simplify

\frac{1}{4} \cdot \frac{( 4 x + 5 ) ^{6}}{6} : \frac{1}{24} (4 x + 5)^{6}

= \frac{1}{24} (4 x + 5)^{6}

Add a constant to the solution

= \frac{1}{24} (4 x + 5)^{6} + C

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

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

\int (sec^{3} (x) tan (x)) d x

\int \frac{7}{( x - 3 ) ( x - 5 )} d x

\int sin^{2} (nπ x) d x