What is the integral from 0 to 1 of t7^{t^2} ?

The integral from 0 to 1 of t7^{t^2} is 3/(ln(7))

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integral from 0 to 1 of t7^{t^2}

\int_{0}^{1} t 7^{t^{2}} d t

\frac{3}{ln ( 7 )}

Decimal

1.54169 \dots

Solution steps

\int_{0}^{1} t \cdot 7^{t^{2}} d t

Apply u-substitution

= \int_{1}^{7} \frac{1}{2 ln ( 7 )} d u

Integral of a constant:

\int a d x = a x

= [\frac{1}{2 ln ( 7 )} u]_{1}^{7}

Compute the boundaries:

\frac{3}{ln ( 7 )}

= \frac{3}{ln ( 7 )}

What is the integral from 0 to 1 of t7^{t^2} ?
The integral from 0 to 1 of t7^{t^2} is 3/(ln(7))