What is the integral of (2x-5)^5 ?

The integral of (2x-5)^5 is 1/12 (2x-5)^6+C

Popular >

integral of (2x-5)^5

\int (2 x - 5)^{5} d x

\frac{1}{12} (2 x - 5)^{6} + C

Solution steps

\int (2 x - 5)^{5} d x

Apply u-substitution

: \int \frac{u ^{5}}{2} d u

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

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{u ^{6}}{6}

Substitute back

u = 2 x - 5

= \frac{1}{2} \cdot \frac{( 2 x - 5 ) ^{6}}{6}

Simplify

\frac{1}{2} \cdot \frac{( 2 x - 5 ) ^{6}}{6} : \frac{1}{12} (2 x - 5)^{6}

= \frac{1}{12} (2 x - 5)^{6}

Add a constant to the solution

= \frac{1}{12} (2 x - 5)^{6} + C

\int (9 + 16 x^{2})^{\frac{3}{2}} d x

\int (cos^{2} (x)) (sin (x)) d x

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

\int \frac{1}{1 - x ^{2} \cdot arcsin ( x )} d x