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Popular >

integral of t(1+t^2)

Solution

\int t (1 + t^{2}) d t

Solution

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

Solution steps

\int t (1 + t^{2}) d t

Expand

t (1 + t^{2}) : t + t^{3}

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of ysqrt(5y+1)

\int y 5 y + 1 d y

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\int e^{\frac{7}{x}} d x

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

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

integral of 2/(2x-7)

\int \frac{2}{2 x - 7} d x

Frequently Asked Questions (FAQ)

What is the integral of t(1+t^2) ?
The integral of t(1+t^2) is (t^2)/2+(t^4)/4+C