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Popular >

integral of 3x^34x^4

Solution

\int 3 x^{3} 4 x^{4} d x

Solution

\frac{3 x ^{8}}{2} + C

Solution steps

\int 3 x^{3} \cdot 4 x^{4} d x

Take the constant out:

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

= 3 \cdot 4 \cdot \int x^{3} x^{4} d x

Simplify

= 12 \cdot \int x^{3} x^{4} d x

Simplify

x^{3} x^{4} : x^{7}

= 12 \cdot \int x^{7} d x

Apply the Power Rule

: \frac{x ^{8}}{8}

= 12 \cdot \frac{x ^{8}}{8}

Simplify

12 \cdot \frac{x ^{8}}{8} : \frac{3 x ^{8}}{2}

= \frac{3 x ^{8}}{2}

Add a constant to the solution

= \frac{3 x ^{8}}{2} + C

Popular Examples

limit as x approaches 1 of 2x^3-4x^2+x+8

x \to 1 lim (2 x^{3} - 4 x^{2} + x + 8)

derivative of 9x+4 derivative of

9 x + 4

y^{''}+2y^'+5y=5sin(2t)

y^{^{''}} + 2 y^{^{'}} + 5 y = 5 sin (2 t)

derivative of y=(e^x+4)^3 derivative of

y = (e^{x} + 4)^{3}

y^{''}-3y^'+2y=e^x+2e^{3x}

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{x} + 2 e^{3 x}

Frequently Asked Questions (FAQ)

What is the integral of 3x^34x^4 ?
The integral of 3x^34x^4 is (3x^8)/2+C