What is the integral from 0 to 1 of 2te^{t^2-1}+3t^7 ?

The integral from 0 to 1 of 2te^{t^2-1}+3t^7 is 11/8-1/e

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integral from 0 to 1 of 2te^{t^2-1}+3t^7

\int_{0}^{1} 2 t e^{t^{2} - 1} + 3 t^{7} d t

\frac{11}{8} - \frac{1}{e}

Decimal Notation

1.00712 \dots

Solution steps

\int_{0}^{1} 2 t e^{t^{2} - 1} + 3 t^{7} 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_{0}^{1} 2 t e^{t^{2} - 1} d t + \int_{0}^{1} 3 t^{7} d t

\int_{0}^{1} 2 t e^{t^{2} - 1} d t = 1 - \frac{1}{e}

\int_{0}^{1} 3 t^{7} d t = \frac{3}{8}

= 1 - \frac{1}{e} + \frac{3}{8}

Combine the fractions

1 + \frac{3}{8} : \frac{11}{8}

= \frac{11}{8} - \frac{1}{e}

\int_{- 1}^{3} x^{2} + 2 x + 1 d x

\int_{1}^{4} \frac{u - 8}{u} d u

\int_{2 x}^{x^{2}} t d t

\int_{0}^{\frac{1}{5}} 4 x d x

\int_{1}^{2} x^{2} + 4 d x

What is the integral from 0 to 1 of 2te^{t^2-1}+3t^7 ?
The integral from 0 to 1 of 2te^{t^2-1}+3t^7 is 11/8-1/e