What is the integral of 10x(x^2+3)^4 ?

The integral of 10x(x^2+3)^4 is (x^2+3)^5+C

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integral of 10x(x^2+3)^4

\int 10 x (x^{2} + 3)^{4} d x

(x^{2} + 3)^{5} + C

Solution steps

\int 10 x (x^{2} + 3)^{4} d x

Take the constant out:

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

= 10 \cdot \int x (x^{2} + 3)^{4} d x

Apply u-substitution

: \int \frac{u ^{4}}{2} d u

= 10 \cdot \int \frac{u ^{4}}{2} d u

Take the constant out:

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

= 10 \cdot \frac{1}{2} \cdot \int u^{4} d u

Apply the Power Rule

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

= 10 \cdot \frac{1}{2} \cdot \frac{u ^{5}}{5}

Substitute back

u = x^{2} + 3

= 10 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 3 ) ^{5}}{5}

Simplify

10 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 3 ) ^{5}}{5} : (x^{2} + 3)^{5}

= (x^{2} + 3)^{5}

Add a constant to the solution

= (x^{2} + 3)^{5} + C

\int_{0}^{1} \frac{33}{x ^{5}} d x

\int e^{- (s - a) t} d t

(3 + x^{5})^{\frac{2}{3}}

\frac{d}{d x} (π \cdot x)

What is the integral of 10x(x^2+3)^4 ?
The integral of 10x(x^2+3)^4 is (x^2+3)^5+C