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

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

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

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

\frac{7}{2} (x^{2} + 5 x)^{2} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int u d u

= 7 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= 7 \cdot \frac{u ^{2}}{2}

Substitute back

u = x^{2} + 5 x

= 7 \cdot \frac{( x ^{2} + 5 x ) ^{2}}{2}

Simplify

7 \cdot \frac{( x ^{2} + 5 x ) ^{2}}{2} : \frac{7}{2} (x^{2} + 5 x)^{2}

= \frac{7}{2} (x^{2} + 5 x)^{2}

Add a constant to the solution

= \frac{7}{2} (x^{2} + 5 x)^{2} + C

\int_{1}^{n} x ln (x) d x

\frac{\partial}{\partial x} ((x^{2} + y) e^{\frac{y}{2}})

\int (4 - x^{2})^{\frac{3}{2}} d x

(\frac{x + 1}{x - 1})^{^{'}}

\frac{d y}{d t} = 5 y

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