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Popular >

integral of 4t^3+t

Solution

\int 4 t^{3} + t d t

Solution

t^{4} + \frac{t ^{2}}{2} + C

Solution steps

\int 4 t^{3} + t d t

Apply the Sum Rule:

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

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

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

\int t d t = \frac{t ^{2}}{2}

= t^{4} + \frac{t ^{2}}{2}

Add a constant to the solution

= t^{4} + \frac{t ^{2}}{2} + C

Popular Examples

derivative of y=10000+30xe^{x/(800)}derivative of

y = 10000 + 30 x e^{\frac{x}{800}}

y^'-4/x y=(y^4)/(x^8)

y^{^{'}} - \frac{4}{x} y = \frac{y ^{4}}{x ^{8}}

integral from 0 to y+z of 1/((z+y+x)^3)

\int_{0}^{y + z} \frac{1}{( z + y + x ) ^{3}} d x

y^'= 1/x y-((x^2)/3)y^4

y^{^{'}} = \frac{1}{x} y - (\frac{x ^{2}}{3}) y^{4}

area x+2y=2,y-x=1,2x+y=7 area

x + 2 y = 2, y - x = 1, 2 x + y = 7

Frequently Asked Questions (FAQ)

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