What is the integral of x(x^2+5)^7 ?

The integral of x(x^2+5)^7 is 1/16 (x^2+5)^8+C

Popular >

integral of x(x^2+5)^7

\int x (x^{2} + 5)^{7} d x

\frac{1}{16} (x^{2} + 5)^{8} + C

Solution steps

\int x (x^{2} + 5)^{7} d x

Apply u-substitution

: \int \frac{u ^{7}}{2} d u

= \int \frac{u ^{7}}{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^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= \frac{1}{2} \cdot \frac{u ^{8}}{8}

Substitute back

u = x^{2} + 5

= \frac{1}{2} \cdot \frac{( x ^{2} + 5 ) ^{8}}{8}

Simplify

\frac{1}{2} \cdot \frac{( x ^{2} + 5 ) ^{8}}{8} : \frac{1}{16} (x^{2} + 5)^{8}

= \frac{1}{16} (x^{2} + 5)^{8}

Add a constant to the solution

= \frac{1}{16} (x^{2} + 5)^{8} + C

\int \frac{1}{6 x lo g _{5} ( x )} d x

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

\int \frac{1}{y} + x d x

\int 2 \frac{4 - t ^{2}}{t ^{8}} d t

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

What is the integral of x(x^2+5)^7 ?
The integral of x(x^2+5)^7 is 1/16 (x^2+5)^8+C