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Popular >

integral of 3(3x+4)5

Solution

\int 3 (3 x + 4) 5 d x

Solution

15 (\frac{3 x ^{2}}{2} + 4 x) + C

Solution steps

\int 3 (3 x + 4) \cdot 5 d x

Take the constant out:

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

= 3 \cdot 5 \cdot \int 3 x + 4 d x

Simplify

= 15 \cdot \int 3 x + 4 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 15 (\int 3 x d x + \int 4 d x)

\int 3 x d x = \frac{3 x ^{2}}{2}

\int 4 d x = 4 x

= 15 (\frac{3 x ^{2}}{2} + 4 x)

Add a constant to the solution

= 15 (\frac{3 x ^{2}}{2} + 4 x) + C

Popular Examples

(dy)/(dx)y=(2x+8)^3

\frac{d y}{d x} y = (2 x + 8)^{3}

integral of e^{4x}sin(2x)

\int e^{4 x} sin (2 x) d x

(\partial)/(\partial x)(4x^3y^2-4)

\frac{\partial}{\partial x} (4 x^{3} y^{2} - 4)

integral of 12x^{5/7}+7x^{-6/7}

\int 12 x^{\frac{5}{7}} + 7 x^{- \frac{6}{7}} d x

y^'=((3x^2+y^2))/(xy)

y^{^{'}} = \frac{( 3 x ^{2} + y ^{2} )}{x y}

Frequently Asked Questions (FAQ)

What is the integral of 3(3x+4)5 ?
The integral of 3(3x+4)5 is 15((3x^2)/2+4x)+C