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Popular Calculus >

integral of tec(2t)

Solution

\int t ec (2 t) d t

Solution

\frac{2 ec t ^{3}}{3} + C

Solution steps

\int t ec \cdot 2 t d t

Take the constant out:

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

= ec \cdot 2 \cdot \int tt d t

Simplify

tt : t^{2}

= ec \cdot 2 \cdot \int t^{2} d t

Apply the Power Rule

= ec \cdot 2 \cdot \frac{t ^{3}}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 ec t ^{3}}{3}

Add a constant to the solution

= \frac{2 ec t ^{3}}{3} + C

Graph

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Frequently Asked Questions (FAQ)

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