What is the integral of x(x^2+3)^7 ?

The integral of x(x^2+3)^7 is 1/16 (x^2+3)^8+C

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integral of x(x^2+3)^7

\int x (x^{2} + 3)^{7} d x

\frac{1}{16} (x^{2} + 3)^{8} + C

Solution steps

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

= \frac{1}{2} \cdot \frac{( x ^{2} + 3 ) ^{8}}{8}

Simplify

\frac{1}{2} \cdot \frac{( x ^{2} + 3 ) ^{8}}{8} : \frac{1}{16} (x^{2} + 3)^{8}

= \frac{1}{16} (x^{2} + 3)^{8}

Add a constant to the solution

= \frac{1}{16} (x^{2} + 3)^{8} + C

\frac{d}{d x} (x^{2} e n (x))

y = tan (3 x)

\int \frac{1}{( x - 7 ) ^{2}} - 1 d x

n = 1 \sum \infty \frac{1}{2 n}

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

What is the integral of x(x^2+3)^7 ?
The integral of x(x^2+3)^7 is 1/16 (x^2+3)^8+C