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Popular >

integral of 4t^3

Solution

\int 4 t^{3} d t

Solution

t^{4} + C

Solution steps

\int 4 t^{3} d t

Take the constant out:

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

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

Apply the Power Rule

: \frac{t ^{4}}{4}

= 4 \cdot \frac{t ^{4}}{4}

Simplify

4 \cdot \frac{t ^{4}}{4} : t^{4}

= t^{4}

Add a constant to the solution

= t^{4} + C

Popular Examples

integral of (x^2-1)/((x^3+x))

\int \frac{x ^{2} - 1}{( x ^{3} + x )} d x

derivative of x^4+8x^2-x

\frac{d}{d x} (x^{4} + 8 x^{2} - x)

integral from 2 to 3 of (3x^2+2x+3)

\int_{2}^{3} (3 x^{2} + 2 x + 3) d x

y^{''}+11y^'+24y=0

y^{^{''}} + 11 y^{^{'}} + 24 y = 0

derivative of (d/(dx(x^5-5))/(x+1))

\frac{d}{d x} (\frac{\frac{d}{d x} ( x ^{5} - 5 )}{x + 1})

Frequently Asked Questions (FAQ)

What is the integral of 4t^3 ?
The integral of 4t^3 is t^4+C